# Have we solved anti-gravity solutions

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Astro-Lexicon G 3

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Degree is a unit of the size of angles in **Degree** to specify. As with the time units of hours, minutes and seconds, this is used to specify angles in degrees *Sexagesimal system*. Therefore the angular degree has 60 arc minutes and the arc minute 60 arc seconds. Accordingly, 3600 arc seconds result in exactly one degree. The symbols to abbreviate these units are **°** for the degree **'** for the minute of arc and **''** for the arcsecond.

In astronomy, the angular degree is generally relevant for specifying angles - degrees are particularly common as the unit for **apparent size** of sky objects. The latitude of the full moon is almost half a degree. That too**Resolving power** of telescopes is given in degrees.

Granulation denotes a very general one *Grit* (lat. *granum*: Grain).

Granulation of star plasma

At **Stars** Granulation means the grain size of the star's surface as a result of convection. See the lexicon entries Photosphere and Sun for details.

Granulation of spacetime

In **Quantum gravitations** like loop quantum gravity (see there for details), granulation refers to spacetime: spacetime is no longer smooth and continuous as in general relativity, but is granular, i.e. it is discretized in quanta, the so-called Wilson loops.

*Gravastern* (engl. *Gravastar*) is a name for a **newer, spherically symmetrical solution** of Einstein's field equations. The name *Grava (c) star* is a made-up word from gravitation (*gravitation*), Vacuum (*vacuum*) and star (*star*). For this reason, the term vacuum stars (*vacuum stars*) choose. Alternatively, but used less often, this new type of object is also called a quasi-black hole. *quasi-black-hole*, QBH). More generally, the gravastars belong to the compact objects in astrophysics.

no singularity & no horizon

Gravastars were made by theoretical physicists *Pavel Mazur* (University of South Carolina, USA) and *Emil Mottola* (Los Alamos, USA) in 2001 as an alternative to the **singular black holes** suggested. They have the amazing property that they are *regular* are, i.e. there are**no intrinsic singularity** at r = 0!

The second, essential quality is that they are **no event horizon** to have. The escape speed therefore always remains just below the speed of light. In other words, the relativistically generalized Doppler factor (redshift factor, **g factor**), which is exactly zero on the horizon of black holes, finite on the surface of gravastars, but is very small, around 10^{-25}! With these objects there is also no horizon **no**Hawking radiation (however, the emission of thermal radiation is to be assumed).

Structure of gravastars: three zones

**1)**In the outer space it corresponds to the Schwarzschild solution for non-rotating black holes. This area is matter-free and asymptotically flat.**2)**Then one closes**thin shell of matter**which consists of an ultra-relativistic quantum fluid, which is a weak source of the gravitational field. Ultra-relativistic means that this matter is on*causal limit*exists: the speed of sound in this medium is exactly equal to the speed of light. The thickness of the layer is of the order of magnitude of the Planck length. This shell is said to have formed during the gravitational collapse of a star or star cluster. Ultimately, it is precisely the shell of matter that prevents the formation of a horizon. If the matter reaches the causal limit in the collapse, a*Quantum phase transition*instead of. The outer Schwarzschild vacuum space-time changes into another relativistic vacuum: the de-Sitter space-time. Even before a horizon can form, the strongly curved space-time (in which there is a lot of energy) goes into a so-called one**gravitational Bose-Einstein condensate (GBEK)**above. This phase transition shows many analogies to the classic Bose-Einstein condensate in solid-state physics. In the case of gravastars, a Bose fluid is chosen as the source of the gravitational field. Therefore, the Einstein-Hilbert effect and that of a scalar field are included in the action functional of the system.**3)**After all, the GBEK is the innermost area of the Gravastern, which has the much larger share of the Gravastern's mass: it is one**Dark energy bubble**! This interior space is also material-free (hence a vacuum) and comes a**de-sitter solution**(positive cosmological constant) that we know from cosmology. The 'bubble' of dark energy stabilizes the thin shell of matter with an outward pressure (see 2) and thus prevents its collapse. A positive cosmological constant Λ means that it is a repulsive force that counteracts the force of gravity: um**Antigravity**. In technical jargon, the transition region between the Schwarzschild and de-Sitter vacuum is also called**Quantum phase interface**. In principle, this 'skin' connects two vacuum states with each other, namely the de-Sitter vacuum inside with the Schwarzschild vacuum or asymptotically Minkowski vacuum outside (up to infinity).

Radiation from the gravastern surface

The equation of state within the shell is very 'stiff'. Shell matter is even more compact than neutron star matter, because the speed of sound here is identical to the speed of light. It is therefore to be expected that **Shock fronts** bounce off the transition layer. The advocates of the Gravastern model see this as a possibility for *Differentiation of gravastars from singular black holes*. Because there are no such rebound effects at (matter-free) event horizons. Other theorists (*Chapline et al.*) calculated that there is a reflection property, so that hard gamma rays are reflected at the transition, but softer photons are allowed through the skin of matter (*transmitted*), i.e. low-energy light is swallowed. The problem is that these calculations state that although gamma radiation is reflected, it is nevertheless strongly redshifted due to the gravitational redshift. This considerably reduces the chance of their detection and the confidence of a verification / falsification.

What happens to incident matter?

The **Accretion of a gravastar** is the subject of current discussions. In the worst case for observation, the collected matter changes in such a way that when it hits the shell, it is converted into the Bose-Einstein condensate inside. As a result, the Gravastern should grow - like the black holes - because it also has a mass parameter. In this scenario, however, observation would be extremely difficult because the ultra-cold shell of matter hardly lights up at all (only very weak heat radiation from a black body). In addition, this weak radiation is then extremely redshifted by the influence of the strongly curved metric.

It is difficult to distinguish

Astrophysicists have to get very close to the compact object with observations, except for about two gravitational radii (equal to a Schwarzschild radius, R._{S.}) in order to be able to distinguish between gravastars and black holes. In both cases, however, the radiation that comes from this area is strongly redshifted. Only black holes are absolutely black and gravastars are 'gray'. Expressed in relativistically generalized Doppler factors, for a Schwarzschild hole g (R_{S.}) ≡ 0 and for a gravaster only g (R_{S.}) ~ 0.

historical background

In itself, the discussion of Schwarzschild-de-Sitter transitions is not new and is based on an idea of *Sakharov* (1965) and*Gliners* (1966) back. In the 1980s, these approaches were picked up to advance cosmology. *Mazur* and *Motto* 2001 took up the forms of the equations of state to calculate the metric of a Gravastern.

You should look there

If gravastars exist, their formation is favored in supernovae of massive stars or in hypernovae or long lasting gamma ray bursts. These stellar explosions are good observation candidates for discovering gravastars. So far, however, there is no consistent model that describes how a massive star could transform into a gravastern. This can only be done with detailed collapse calculations.

future research projects

According to the Birkhoff theorem, the spherically symmetric Gravastern is necessarily **static**. In the light of astrophysics, this is a disadvantage of the gravastars, because precisely the **rapidly rotating black holes** (described by the Kerr solution of ART) explains many astronomical observations satisfactorily:

A generalization of the Gravastern solution to the *rotating case* is therefore desirable, but has not yet succeeded.

Another aspect is that it is not enough for a spacetime solution to Einstein's field equations - it must also be shown that the solution is **stable** is. If this is not the case, this state is not even reached in nature. The stability of gravastars has not yet been demonstrated convincingly either.

Gravastars with anisotropic pressure

On the contrary: Current studies show that Gravastern models, which consist entirely of an ideal liquid, fail: Either they would swell to infinite size, or a horizon would form after all. From the point of view of New Zealand gravitational researchers, the solution to this stability problem is a **Gravastern with anisotropic pressure** (*Cattoen, et al.* 2005). This means that the pressure in the Gravastern is not the same in all directions. The anisotropy must be guaranteed in the Gravastern shell. However, the property of negative pressure in the interior is retained. Continuous solutions with isotropic pressure (like the original Gravastern model according to Mazur and Mottola) always have a pole in the pressure as a function of the radius. This creates an unphysical, naked singularity. This is a new finding in gravastern physics.

skeptical community

The reactions of astronomers to Gravastern models are quite subdued. For some it is what they have been waiting for forever, for others it is just another academic (i.e. superfluous) solution to the Einstein equations. The same applies to another alternative to the black hole that has some similarities to the Gravastern, namely the Holostar (*Petri* 2003).

In this area, therefore, a lot has to be researched both on the part of theory and on the part of observation. In any case, it is a hot lead, the pursuit of which will help solve the mystery of the black holes. Classical black holes also have properties that give physicists a headache - especially their curvature singularity. This 'point of infinite curvature' is perhaps just an artifact of the classical GTR description. There are the singularity theorems of *Roger Penrose* and *Stephen Hawking*that enforce the existence of singularities; but these theorems require certain conditions. The Gravastern does not contain a singularity and is therefore in contradiction to the singularity theorems. Does that disqualify the new proposal? Or does that rather signal that the singularity theorems need to be revised? Because one can also question the prerequisites of the theorems. This conflict is the subject of current research.

Further literature

*Mazur, P.*&*Mottola, E.*: Gravitational Condensate Stars: An Alternative to Black Holes, Preprint: gr-qc / 0109035*Cattoen, C., Faber, T.*&*Visser, M.*: Gravastars must have anisotropic pressures, Class. Quant. Grav. 22, 4189 (2005), preprint: gr-qc / 0505137- Web article: Black Holes - The Darkest Secret of Gravity

Gravitation (lat. *gravitas*: Gravity) is one of the four fundamental forces in nature: gravity.

The weakling among the fours

Of all four basic forces, this force is the one that is particularly familiar to us. The other forces are the electromagnetic force, strong and weak - the latter two play a special role in the subatomic area and are important to understand the cohesion of the matter around us.

If one compares the strengths of the four fundamental forces of physics, e.g. with the help of the *Coupling constants*so it becomes clear that gravity **the weakest of all forces** is. Because of this fact, a roof tile falling from a house does not come to the center of the earth, but splinters on the ground: the electromagnetic forces between the atoms of the brick and the ground have caused a sudden repulsion, a force called gravity could not overcome. Even stronger than electromagnetism is the strong force, which even manages to hold protons of the same type of electrical charge together in an atomic nucleus. We owe the diversity of chemical elements to the strong force, but also to the weak force (radioactivity).

The weakling dominates

But the attribute weak is not synonymous with unimportant: Gravitation is the dominant force on the very large length scale - as soon as we speak of astronomical units, light years or even billions of parsecs. Because gravitation and electromagnetic force have one **infinite range**! But in contrast to electromagnetism, gravity has the property that it is itself **do not shield** leaves. The consequence is:

Gravity dominates the universe.

It is what shapes the large-scale structures: it makes the planets dance around the sun in elliptical orbits, it compresses massive stars into black holes at the end of their existence, and it even makes galaxies and galaxy clusters merge.

But what exactly is gravity?

As familiar as we are with gravity in everyday life, it is also puzzling. It is by no means easy to understand what the**Nature of gravity** is. Even in the 21st century, physicists and astronomers know a lot about gravity, but even today we are far from understanding everything. Is gravity a force at all?

In the next few sections, we'll tackle nearly 2,400 years of human thought that emerged as significant to understanding gravity. That is certainly a bit of a hassle, however *Gravity* is an essential term in physics and therefore also in this lexicon. Hopefully at the end of the reading you will have an idea of what gravity actually is.

Ancient thought leader: Aristotle

To be a well-documented pioneer of gravity research, one has to be a Greek scholar *Aristotle* (384 - 322 BC) count. Aristotle is actually better known as an important humanities scholar than a student *Plato* and as an educator *Alexander the Great*. However, Aristotle also tried to explain the movement of the sun, moon and the planets known at the time by using very simple models. The **resting earth was in the center** of this model (*geocentric worldview*), and around them circled the sun, moon and planets. The **circle** as a perfect, geometrical figure represented the basis to understand the movements of these bodies as circular movements. This explained the roughly periodic repetition of the movement of the stars. Because once the circular path ended, the cycle began again. The stars were viewed as motionless fixed stars. Without precise measurements and observations, this model was consistent with the nature observations. Since it was in harmony with church teachings, this Aristotelian view of the world survived for many centuries.

Aristotle tried that too **Movement of falling bodies** on earth to explain. For him, the straight fall path was proof that the earth was at rest. These first considerations with the principle of 'nature observation - explanatory model' are already in the spirit of the Enlightenment epoch almost 2000 years later (experiment - theory). Aristotle thus presents the first (if not entirely convincing) phenomenological models for gravity.

The epicyclic model according to Ptolemy

A small modification was made to the model for the movements of the sun, moon and planets by the Alexandrian scholar*Claudius Ptolemy* (100 - approx. 160 AD). He is the author of the **first standard work of astronomy**, that under the name *Almagest* got known. That too *Ptolemaic view of the world* is geocentric and based on Circular orbits - however, complexity was brought into play by the fact that the centers of circular orbits are themselves circles, the so-called *Speakers*, move. The circle on the speaker is called **Epicyclic** (Greek for 'overcircle'). An illustration of this simple, geometric model is shown in the figure on the left. On the one hand, the model preserved the special role of the circular figure, which the Aristotelians regarded as perfect; on the other hand, the epicyclic model is able to explain more complicated movements: That was already the case back then *retrograde movement* (e.g. with Mars), which was completely incomprehensible in the Aristotelian worldview. As the illustration shows, the resulting orbital shape of the planet shows loops in which the planet is moving backwards as seen from the earth. The Ptolemaic epicyclic theory therefore explained the observed decline. But unfortunately not all movements of the celestial bodies could be described consistently with epicycles.

Galileo - gravitational researcher and pioneer of astronomy

The Italian physicist, mathematician and philosopher *Galileo Galilei* (1564 - 1642) is the first to systematically and mathematically research gravity. Galileo should **Trap experiments** at the Leaning Tower of Pisa to test his hypothesis as to whether a body's weight or density determines how quickly the body falls. Galileo also carried out numerous mechanical experiments **Commute** and with rolling objects on the **inclined plane** by. He explained that **Path of projectiles in the gravitational field** by superimposing two movements, namely a uniformly accelerated falling movement and a uniformly straight movement of the bullet (*Superposition principle*) and proved the **Parabolic path**. **Side notes:** Galileo Galilei is significant and known for his astronomical discoveries: he improved the Dutch telescope, the *Hans Lipperhey* invented and observed for the first time in 1610 the craters of the moon, the composition of the Milky Way from stars and four moons of the giant gas planet Jupiter (*Galilean moons*). His discovery of the phases of Venus confirmed the Copernican, heliocentric view of the world in observation. The rapture of the earth from the center of the world and the acceptance of its movement led to an open dispute with the Catholic Church. In 1633 Galileo was summoned to Rome on suspicion of heresy, and in the same year he renounced the heliocentric doctrine. In 1992 Galileo was officially rehabilitated by the Catholic Church by Pope John Paul II. *Albert Einstein*, to which we will come later in the course of this encyclopedia, wrote about Galileo:

All knowledge about reality starts from experience and flows into it. Sentences obtained purely logically are completely empty with regard to the real. Through this knowledge, and especially through the fact that he hammered it into the scientific world, Galileo became the father of modern physics, yes, of modern natural science in general.

(taken from *The classics of physics*, P. 334, Verlag Hoffmann and Campe, 2004)

Newtonian gravity

The study of gravity has been carried out by the English polymath *Sir Isaac Newton* (1643 - 1727) achieved a major breakthrough. Newton became famous for many achievements: the foundation of differential and integral calculus, discoveries in optics (color theory, corpuscular theory of light) and the theory of gravity that is named after him today. The**Newtonian gravitational physics** is the first theory of gravity to deserve the name theory because it is a consistent, comprehensive concept and not just phenomenology or hypothesis. Newton introduced this theory in his work *Philosophiae naturalis principia mathematica* this work *Principia* is the very first standard work in theoretical physics! The title is a reply to that *Principia Philosophiae* of *René Descartes*.

Newton devoted himself to optics and gravity in 1665. The story of the tree **falling apple**, who hit Newton in the head and inspired him to the theory of gravity is probably a myth - Newton only wrote that a falling apple made him think about gravity. At the age of 27, Newton became (on the recommendation of the predecessor of this office) Lukas professor of mathematics - a chair at Cambridge University, which incidentally is today *Stephen Hawking* holds. Newton knew the astronomical observations from *Johannes Kepler* and his discovery that the planets move on elliptical orbits around the sun. In 1666 Newton began to look for a physical explanation of these purely empirical Kepler laws. Kepler's second law (*Area set*) he was able to explain in 1679 that there was a **attractive central force** must give that emanates from the sun.

A meeting of three members of the *Royal Society* in 1684 was to be the key event: This is where Newton's adversaries met*Robert Hooke*, the astronomer *Edmond Halley* and the architect *Christopher Wren*. They discussed a force that is proportional to the inverse square of the distance and that determines the planetary motion. Inspired by this discussion, Halley asked Newton about the shape of a celestial body orbit that results from this law of force. Newton had already calculated this question years earlier and knew that it had to be an elliptical orbit. The detailed elaboration of this calculation ultimately led to Newton's one and a half year creative phase and the publication of the *Principia* 1687.

The book I the *Principia* contains the three laws of motion nowadays known as *Newton's Laws* be taught, namely that**Law of inertia**, the **dynamic constitution** and the **Reaction principle** (*actio = reactio*). The dynamic basic law shown in the equation on the left is much better known in school physics **F = m a**, but this case only applies if the mass is time*U.N*dependent, **m** ≠ **m (t)**, is. In general, however, this is not the case (e.g. with the so-called*Rocket equation*: a flying missile loses fuel and therefore mass), so the law as the time derivative of the momentum **p** must be formulated. Book II is a textbook on fluid mechanics. Finally, Newton notes his be in Book III**Law of gravity** and demonstrates the validity of this theory of gravity using the movements of planets and comets.

Newton's theory also states that **Instantaneous gravity** spread out, i.e. without delay. Besides, time and space have one **absolute character** in Newtonian physics. In the next section we will see that these properties of gravity turn out to be untenable and that Newtonian gravity must be generalized to Einstein's gravity.

Einstein's general theory of relativity

Presented in 1916 *Albert Einstein* (1879 - 1955) a completely new view of gravity. In that year he published the General Theory of Relativity (ART), an (unquantized) theory of gravity that describes gravity not as a force, but as a**geometric property of space and time** understand. This theory of gravity was preceded by the special theory of relativity (SRT), which is not a theory of gravity, but which introduced the revolutionary redefinition of the terms energy, mass, time and space. According to Einstein, space and time are linked to form a four-dimensional structure: space-time. While spacetime is still flat in the SRT, it is curved in the GTR. How to simplify in a two-dimensional variant a **curved spacetime** can imagine, shows the figure on the left. The 'bump' in this 2D space-time is caused by masses. Einstein already recognized in the SRT that energy and mass are equivalent, which in the famous formula E = mc^{2} is summarized. The consequence: masses and all forms of energy cause 'bumps' in spacetime. A (force-free) movement through space-time is now not possible in any form, but only along certain curves, which in the GTR**Geodesics** to be named. The geodesics 'meander' through the 'dented space-time' - exactly how this happens is dictated by the mathematical laws of differential geometry. We take the movement along the geodesics as gravitation. So we move daily under the influence of the curved space-time!

The achievement of abstraction is enormous in order to be able to halfway grasp this new picture of gravity. Nobody can imagine a four-dimensional, curved spacetime, but if one suppresses some dimensions, at least one can **Space-time diagrams** draw that will help you understand. Einstein's new theory of gravity can be summed up in a single but unfortunately complicated formula: the **Field equations of the ART**. This clear equation is on the right (here for the sake of simplicity without the cosmological constant Λ). In this concise form, the formula directly states that the curved spacetime that is in **G** is of mass and energy that is in **T** stuck, is caused; the equation also includes the aspect that the bumps in spacetime dictate motion. However, the simplicity of this formula is deceptive! Behind the symbols **G** and **T** hide math objects that **Tensors** to be named. More precisely is **G** the Einstein tensor and **T** is called the energy-momentum tensor. In general, these objects are very complicated, consist of several components and vary from spacetime point to spacetime point.

A gravitational field in Newtonian physics is now replaced by spacetime in Einsteinian physics. Spacetime is the solution of Einstein's field equation and is clearly described by the metric (the metric tensor **G**) or alternatively by the line element. The gravitational force of Newton is replaced by the Christoffel symbols, the Riemann tensor and other mathematical quantities of ART (1-forms, 2-forms, Killing fields, Kretschmann scalar, Ricci tensor, Ricci scalar etc.). It is often of interest how test objects move through a curved space-time. To solve this problem, the **Geodesic equation** be solved. For light, this process is called relativistic ray tracing.

Spacetime are in general too *dynamic*, i.e. they are constantly changing their curvature properties. This happens especially with **Gravitational waves**which can also be described with Einstein's theory. They are bumps in space-time that move with the speed of light in a vacuum *c* spread. This is an important difference to Newtonian physics: In Einstein's theory, gravitation does not propagate arbitrarily quickly, but precisely with it *c* out.

Einstein's ART has proven itself many times in experiments. A number of experimental tests and successes as well as the theory itself are presented in great detail in the dictionary entry General Theory of Relativity.

relativistic astrophysics

Einstein's theory also had a strong influence on astronomy: Many astrophysical processes can only be treated satisfactorily with Einstein's gravity. The gravitational collapse into a compact object (e.g. neutron stars) is an example of this. Models based on the ART have been established in accretion physics. But even on the very large spatial scale, Einstein's theory is the right choice: cosmology is relativistic. The entire universe can also be understood as a solution to Einstein's field equation and described using the Robertson-Walker metric. The Friedmann world models that emerge from the GTR describe an excellent number of observations of experimental cosmology (see cosmic background radiation, supernovae type Ia). A number of observed phenomena cannot be understood in the context of Newtonian gravity, e.g. gravitational and cosmological time dilation, redshift and gravitational redshift as well as frame dragging.

cosmological significance of gravity

The importance of gravity for the entire universe is based on two properties that were already mentioned at the beginning: In principle, gravity has one **any range**, And she is **not shield**. Due to the first property, gravity can also act over extremely large distances - up to billions of light years, i.e. scales as large as the cosmos itself. Due to the second property, non-shieldability, there is hardly any possibility of stopping gravitation (unless through Antigravity - more on this in the next section). The consequence is what astrophysicists do **gravitational instability** call. This can be clearly described in such a way that the matter begins to 'clump' due to the influence of gravity: If the jeans mass is exceeded locally for a mass accumulation, the gravitational collapse begins. Later this lump fragments into smaller ones. These scenarios are essential to the origin of the **spacious structure** to understand in the cosmos. From the initial distribution of the 'primordial gas', which arose in the primordial nucleosynthesis, the first generation of stars (Population III) was formed through gravitational instabilities. The first galaxies arose from the influence of gravity - at least that's how it went in one of them **hierarchical growth scenario** from.

Antigravity

Relativistic cosmology has spawned a form of gravity that makes science fiction fans' eyes wet: **Antigravity**. To explain the context, we need to take a look at modern cosmology. The dynamics of the Friedmann world models already mentioned are determined by the forms of energy in the cosmos. The 'normal', baryonic matter, of which we are made up, is a form of energy, but its meaning is practically irrelevant. Another form of matter, dark matter, is much more common in the universe. It influences not only the dynamics and development of galaxies, but also of the cosmos as a whole. Their relative share is around a third. What exactly is hidden behind dark matter, however, is a mystery - the current ideas are presented in the entry Dark Matter.

Now we come to the crucial part: the remaining two thirds of the energy in the universe is accounted for by the **Dark energy**. What exactly is behind this mysterious, cosmic ingredient is an explosive and highly topical research area. It is not a concrete form of matter, but rather the physicists favor that the quantum vacuum, which is finely distributed throughout the universe, manifests itself as a cosmologically relevant form of energy. The astronomical observation fact is one **accelerated expansion** of the cosmos. In the standard model of cosmology this is explained by the existence of dark energy (alternatives are shown in the entry dark energy).

The special thing about dark energy is its equation of state, because it unites **negative pressure** having. That sounds very unphysical, but it explains the observations surprisingly well. According to astronomical observations, the so-called w-parameter is close to **w = -1**. Thus, from a whole range of models for dark energy, a certain one is obviously preferred by nature, namely the**cosmological constant**which none other than Einstein introduced in 1917. It just has the right w-parameter - and it does not vary over time, which also fits with current observations on distant, exploding white dwarfs. Such an equation of state ensures an expansion of the universe, which can be understood as antigravity. Because dark energy counteracts gravity. Using the Friedmann equation one can show that towards later development epochs the influence of the anti-gravitational dark energy increases. The current data predicts an eternal and ever faster expansion of the universe. In the end there is a **cold cosmos**, in which probably only black holes (with different masses and angular momentum) and maybe black dwarfs still exist.

Quantum-level gravity

However, Einstein's gravity also has its limits. The attentive reader will not have missed the fact that the ART with the attribute *unquantized* was provided. This means that the concepts of the second great physical theory of the 20th century, quantum theory, did not find any consideration in Einstein's theory.This did not happen out of ignorance: Einstein would have liked to have invented such a comprehensive field theory; in fact, he worked on this overarching theory in the last few years of his life - but the challenge was too great even for Einstein.

Such a quantized theory of gravity is labeled **Quantum gravity** Mistake. The motivation for this is that quantum effects also become important in gravitational processes, namely when **strong gravity and small length scale** getting together. Where does this happen in nature? It happens with objects that are dominated by gravity and that are very compact, namely with **Black holes**. According to Einstein's ART, a point-like object lurks in every black hole, in which the curvature of space-time increases immeasurably. These fantastic places are called curvature singularities (and must be strictly distinguished from coordinate singularities!). But are there actually points in nature? The concepts of quantum theory negate that. The physics of black holes is a first motivation to dare to work out a quantum gravity.

A second motivation is provided by the cosmology of the early universe: the high-energy physicists have discovered that our world of the four natural forces was not to be found in the young cosmos. The temperature environment led to some forces 'fusing' with one another: the hotter it is, the less fundamental natural forces are present. The 'summit' of this**Unification** is said to have prevailed as a primal force in the Planck era. Gravitation was said to have been the first to split off from the primal force with expansion and the resulting cooling. The experts call this transition **Symmetry breaking**. After the first symmetry break, there were two fundamental natural forces: gravitation and X-force in the so-called GUT era. The question that drives the high-energy and particle physicists is how to combine gravity with the other quantum forces *uniformly* could describe as quantum field theory.

In the quantum picture, gravity is neither a force nor a curved space-time: it is a gauge boson. This is what quantum field theorists call quantized 'messenger particles' that convey the force. In the case of gravity, this exchange particle also has a name, namely **Graviton**. The properties of gravitation require some properties of the graviton, e.g. that it have spin 2 *got to*. Much excitement therefore arose when a theory was discovered in the 1970s that contains spin-2 particles. This theory was one of the first variants of the**String theories**. With this, string theories suddenly became the most interesting candidate for quantum gravity. Even in the 21st century, string theories are one of the most active areas of theoretical physics. As explained under the entry String Theories, this research is caught in a rollercoaster of successes and doubts. One problem is, for example, that this messenger particle of gravity has not yet been discovered experimentally. On the success side, string theory can boast a modern view of gravity and calibration: This is how the**AdS / CFT correspondence** discovered, which points to a deep connection between gravity and particle theories. In the meantime the principle has been generalized and is currently being researched (*gauge / gravity duality*). Further successes are models which are under the designations **Branenworld** gather. These models, for example the Randall-Sundrum models or the Cyclic Universe, have quite astonishing properties and are able to explain in a very elegant way what was previously not understood (coincidence problem, weakness of gravity, smallness of the cosmological constant, cause of the Big Bang, etc.).

Another variant of quantum gravity was added in the 1980s, which takes a slightly different approach. Close to the concepts of Einstein's gravity (see e.g. under the tongue twister, diffeomorphism invariance), emphasizes the **Loop quantum gravity** (LQG) the geometric character of gravity. Within the framework of this theory, the quantization of space-time in so-called Wilson loops has actually succeeded. With the concepts of the LQG, the singularities of the GTR can indeed be eliminated! This applies to both the curvature singularity of black holes and the big bang singularity. The theory and its prognoses are presented under the entry loop quantum gravity.

String theories and loop quantum gravity are the two major contenders that have the potential to expand Einstein's gravity. The skeptic may object that so far there is no convincing evidence from experiments that would give these quantum gravity the status of a proven theory of gravity. That is the major difference to the theories of Newton and Einstein. However, gravitational researchers remain very active in providing this evidence. Important new impulses are expected from the state-of-the-art particle accelerator facility: the *Large Hadron Collider* (**LHC**).

Approximate, speculative & exotic

With what has been said so far, the entry on gravity could actually close, but something should also be said about theories of gravity outside the mainstream. The following are intended to **approximate and alternative theories of gravity** be briefly presented.

Theories of gravitation with torsion

In the case of the theories of gravity with torsion, the torsion tensor does not vanish. The ART, on the other hand, is *torsion free*, What *symmetrical* Christoffel symbols. In the case of gravitation theories with torsion, one deals with additional terms that do not even exist in GTR. This makes these alternatives more complicated than the ART.

Far parallel gravity

Far parallel gravitation or short **Distant parallelism** was introduced in 1928 by Einstein as a new theory of gravity *With* Invented torsion. In this theory, gravity is not a result of the curvature of space-time, but rather a result of the twisting of space-time (torsion). The gravitational researchers were able to show that distant parallelism and ART as *equivalent formulations* gravity can be understood. Currently, gravitation theorists are publishing the corresponding far-parallel counterparts to the usual solutions of the ART field equations.

In modern gravitational physics, attempts are also made to construct other forms of distant parallelism, the *Not* can be understood as analogous to GTR. In these far-parallel theories of gravity *teleparallel gravity*) completely new insights into the nature of gravity can be gained. The hope is to find in this way a theory of gravity that is superordinate to Einstein's theory or to be able to draw interesting cross-connections to gauge, field and quantum gravity theories.

Scalar tensor theories

The scalar tensor theories are based on the idea that in addition to the metric tensor, a *additional***Scalar field** is available. This field couples to the curvature scalar (*Ricci scalar*), but not the metric tensor. The GTR can be derived from an effect functional that is found in the literature*Einstein-Hilbert effect* is called. A scalar field is missing here. The action functional of the scalar tensor theories accordingly contains additional terms. The scalar field can now be equipped with different properties: it can be constant in every space-time point, or it can vary. In the case of a variation, it can be said that Newton's gravitational constant *G* now *no fundamental natural constant* is more. There are many variants of the scalar tensor theories. The best known is the **Brans Dicke Theory**.

MOON theory

The MOON theory (see there for details), published in 1983 by the Israeli physicist *Mordehai Milgrom* was invented is a theory of gravity that corrects Newton's law of gravity by an additional factor. This factor depends on the acceleration and can explain the rotation behavior of many spiral galaxies very well - astonishingly *without* Dark matter.

TeVeS

TeVeS is, so to speak, an 'offshoot' of MOND, because it was discovered from the relativistic expansion of MOND. *Jacob D. Bekenstein* has this in 2004 * Tensor-Vektor-S.kalar theory of gravity* formulated, which, so to speak, goes one step further than the scalar tensor theories, because an additional vector field is included. Current studies show that TeVeS can explain many observations of modern cosmology in the same way as Einstein's theory. However, this quite new theory is controversial and is only at the beginning of a lengthy evaluation and testing process.

Post-Newtonian approximation

The so-called post-Newtonian approximation of Einstein's gravity is obtained when one carries out the limit v / c «1 from GTR to Newtonian physics, **but terms of the linear order v / c** leaves. Pseudo-Newtonian (**PN**) Gravitation is something like a 'hybrid gravity between Einstein and Newton'. It is particularly useful in celestial mechanics when sufficiently good results for orbital movements are desired, but cannot or should not be fully relativistically calculated. The determination of the approximate gravitational equations are quite complex, but can be implemented very easily in computer code to solve the gravity problem. PN codes are often used to calculate phenomena with gravitational waves. To increase the accuracy and thus to approximate Einstein's gravity even better, the corresponding order v / c can simply be increased, e.g. PN 5th order.

An analogous methodology is used by gravitation researchers to approximate other gravitation theories, e.g. a scalar tensor theory. This underlines the universality and usefulness of the approximation method.

Pseudo-Newtonian gravity

In the context of pseudo-Newtonian gravity, an approximation to Einstein's gravitational physics is sought. Point masses are described relativistically with the Schwarzschild solution. The pseudo-Newtonian approach consists of a 1980 of *B. Paczynski* and *P. Wiita* proposed model that mimics the gravitational field of a point mass. For this purpose, the typical and mathematically complex tensor notation is not used, but the potential formulation, which looks like Newtonian gravitational physics. The main difference is that not the usual Newtonian potential is used, but the so-called **Paczynski-Wiita potential**. This new potential scales with the Schwarzschild radius and can accordingly to a certain extent simulate the gravitational effects around a point mass and in particular the effects near a static black hole. The accuracy with which the relativistic effects can be imitated is about 10-20%, provided that radii outside the marginally stable orbit (here with six gravitational radii) are considered.

Gravitation with extra dimensions

An interesting variant of a theory of gravity are those **Field theories with extra dimensions**. These are the theories that allow further space dimensions, but not further time dimensions. The special thing is that gravity also acts in the higher spatial dimensions - but not the other natural forces. This explains gravitational theories with additional spatial dimensions, which are also used in modern language **Brane models** very elegantly the hierarchy problem in physics.

The first proposition historically was that **Kaluza-Klein theory**which, as a 5D field theory, aimed to unify electromagnetism and GTR. The theory failed at that time, but contains aspects that are also of interest today (within the framework of string theories), e.g. the compactification of the extra dimensions. Interestingly, some theories with extra dimensions can be reduced to the form of scalar tensor theories. In other words, the properties of the extra dimensions can be identified as a scalar field. Examples of this are the radion or dilaton.

The following industry models are presented in detail in the knowledge portal: **ADD scenario**, the **Randall-Sundrum models**, the **DGP scenario** and the**Cyclical universe**. All models provide valuable, new insights into new physical territory. However, it is not yet clear whether this form of physics is actually implemented in nature. The clarification of the Pioneer anomaly may bring new insights in this regard.

f (R) -gravity

The f (R) -gravity (see this entry for details) is a modification of Einstein's ART. Be functional in the effect **nonlinear additional terms** takes into account any dependency on the**Curvature or Ricci scalar***R.* can have - hence the designation f (R). The dynamics of gravity is determined by a field equation that results from this new action functional. The non-linearities create new effects, for example, that gravity can lead to a significant or even accelerated expansion of space-time even with weak curvatures. The latter aspect makes the f (R) model interesting for cosmology because an f (R) scenario could take on the role of dark energy. Currently there are many **f (R) families** presented, analyzed, falsified and their importance for gravitational research, astrophysics and cosmology explored. In order for this alternative to establish itself, many successfully completed practical tests are still necessary.

Importance of gravity for humans

If you want to get to the heart of the billions in the development of the universe, you will see the following: We not only experience gravity every day as a force that keeps us on the ground, but its very subtle and unique properties that distinguish it among all natural forces responsible for our being here at all! The effects of gravity on our life manifest themselves in many aspects: The life-giving energy of the sun would not even exist without gravity; the course of the stars, which shaped our culturally solidified cycles such as day, month and year, is also a product of gravity; without gravity, the earth would not have an atmosphere whose gases have enriched the evolution of life with a fantastic variety - this list goes on. We should draw the conclusion from this to become a bit more down-to-earth and not to take off, but to meet the weighty influence of gravity with humility, but not with melancholy.

Literature tips

- C. W. Misner, K. S. Thorne & J. A. Wheeler:
**Gravity**, Freeman San Francisco, 1973 **The classics of physics - E = mc**, Verlag Hoffmann and Campe, 2004^{2}

In general, in astrophysics, it means the collapse of a massive object under the effect of its own gravity.

Look what's collapsing there

During the evolution of the stars, a cold gas, dust and / or molecular cloud collapses into a protostar when it reaches a critical mass - the so-called jeans mass.

In 'normal' stars the gravitational pressure is compensated by gas, centrifugal and radiation pressure: the star is in hydrostatic equilibrium. The gravitational collapse of 'dying' stars is important in this context. This is how astronomers describe the end of the normal stellar phase and the transition to a compact object. The collapse starts when the internal, thermonuclear fusion processes end and the nuclear fire goes out. The residual star collapses in free fall under the effect of its own gravity. At first the gravitational pressure gains the upper hand, but can possibly be stopped.

The mass does it

What happens to the collapsing star depends on its **Mass and composition** (see figure above). In the gravitational collapse, the matter is compressed more and more. In doing so, it can change its properties significantly. Physicists call these mostly sudden changes **Phase transitions**. *phase* is a term used in thermodynamics (thermodynamics). An example of a simple phase transition known from everyday life is boiling water: water that is liquid at room temperature - the liquid phase - boils at around 100 degrees Celsius and evaporates - into the gaseous phase. Something similar happens with the phase transitions of collapsing stellar matter.

Final state 1: white dwarf

Due to the Pauli principle of quantum theory, particles with half-integer spin, the fermions, cannot be compressed to any degree.This affects first of all the electrons in the collapsing stellar matter, which are fermionic. The Pauli ban takes care of the at high densities **Degenerative pressure of the electrons**. If the collapse matter does not weigh more than 1.46 solar masses (with a slight dependence on the composition), the degeneracy pressure can withstand the gravitational pressure and bring the system into equilibrium! The critical mass limit just mentioned is called Chandrasekhar mass after the Indian astrophysicist who discovered it. The stellar objects stabilized in this way are called white dwarfs. These objects are very hot and therefore have a white glow (see effective temperature). They owe the second addition to their name, dwarfs, to their small size: They only have a diameter comparable to that of the earth, but typically weigh as much as the sun! This first possibility for a compact object after the gravitational collapse can be seen in the picture on the left. White dwarfs slowly cool down and eventually turn into black dwarfs. However, this process takes a good 10 billion years, which is comparable to the age of the universe. The age of a white dwarf can be drastically reduced if it exceeds the Chandrasekhar mass by collecting matter (accretion), for example from a nearby companion star: Then the white dwarf explodes in a spectacular star explosion that leaves nothing behind. This explosion is a Type Ia supernova and is of great importance to cosmology.

Final state 2: neutron star

With higher residual masses of the collapsing stellar matter, the degeneracy pressure of the electrons can no longer do anything. At the immense densities, the electrons are literally pressed into the atomic nuclei; nuclear physicists call this an inverse beta decay. The consequence of these nuclear physical transformation processes at the subatomic level is this **Neutronization** of matter. Now the star matter has completed a phase transition and completely changed its properties. However, neutrons are also fermions, so that the degeneracy pressure of the neutrons stabilizes the collapsing star. In addition to neutrons, there are a number of exotic particles (hyperons, kaons, diquarks, and finally even free quarks, as astrophysicists suspect) that form at even higher densities. The even more compact object stabilized in this way is called a neutron star. It also weighs about as much as the sun, but is only about 20 kilometers in diameter! The upper mass limit for neutron stars has been controversial among experts for years: A conservative value is two to three solar masses, which follows from the theory of relativistic, compact stars (*Nauenberg* & *Chapline* 1973; *Rhoades* & *Ruffini* 1974). In the meantime, significantly smaller limiting masses are also being discussed, e.g. 1.5 to 1.8 solar masses (*Burgio* 2004). The stumbling block is the equation of state of neutron star matter: It is simply still unclear what happens in detail with such compact matter. The inhomogeneous shell structure of different forms of matter inside the neutron star makes the theoretical description extremely complicated. Observational astronomy can provide valuable information on this controversial question because in many cases it is possible to measure the masses and radii of candidate neutron stars in the sky. These parameters result in properties of the internal structure that could favor a theoretical model.

Neutron stars can be found in the middle of the first figure above. Neutron stars are already highly relativistic objects. They are quite effective in catching, weakening and reddening light based on Einstein's general theory of relativity. This phenomenon is called gravitational redshift. Therefore, neutron stars are shown in dark red in the picture. As a rule, neutron stars are discovered by astronomers when a sharply focused cone of radiation, which is created close to the neutron star's surface, hits the earth. These neutron stars are called pulsars. Neutron stars can also have particularly strong magnetic fields and are then called magnetars.

Final state 3: black hole

But there is also the ultimate compact object that surpasses a neutron star in compactness and mass: a stellar black hole. Theoretically, they are described with the general theory of relativity (GTR) and are used here under the names Schwarzschild solution (non-rotating) and Kerr solution (rotating). One of the greatest secrets in astrophysics is what exactly happens to matter when it collapses into a black hole. In the context of relativity, which is a classical, unquantized theory, black holes have singularities deep inside. They are the source of gravity because from the theory point of view the rest of spacetime is 'empty'. The collapse to a black hole is the collapse to one point! The gravitational redshift near the hole is so strong that any radiation emission is suppressed. This marks the event horizon and makes the holes black. The horizon obscures the intrinsic spacetime singularity (so-called *cosmic censorship*). In a singularity the curvature becomes infinite (see also Riemann tensor and Kretschmann scalar) and a physical description collapses. In the context of the classical GTR, one can only say that there is 'mass without matter' in the singularity. In a black hole, matter has lost all properties except for mass and angular momentum. The no-hair theorem, that of the relativist, takes this fact into account *John A. Wheeler* was established. It is also he who sees the collapse of classical physics in the appearance of the curvature singularities. Perhaps singularities show that this is where the area of responsibility of a completely new physical theory begins.

Modern physics already knows such theories as string theories and loop quantum gravity, which try to go beyond classical GTR. On the basis of these current findings, new approaches for the vacuum and quantum vacuum emerge. To put it cautiously, the new theories could herald the end of classic black holes, as the currently discussed alternatives holostars and gravasters suggest - but the physicists are not yet ready.

Everyone should see it: spectacular transformations

The formation of white dwarfs is relatively unspectacular: the low-mass forerunner star, which is comparable to the sun, expands to become a red giant and loses its outer star shells, which form a planetary nebula. The rest of the star matter collapses, leaving behind a white dwarf.

For the formation process of the last two types of compact objects, neutron stars and stellar black holes, the precursor star must be very massive. 8 to 20 solar masses are typical. The final scenario is catastrophic: In gravitational collapse, a shock wave runs into the interior of the star. In the core there is already a highly compressed star core, the particularly ferrous pre-neutron star. The incoming shock wave is applied to this dense matter. *hard core*) reflects and runs outwards again. There it tears up the outer shells of the stars and causes the star giant to explode inside one**Type II supernova** (engl. *core-collapse SN*). The inner part collapses and forms a neutron star. If more mass collapses, the gravitational collapse proceeds in a similar way, only the explosion becomes even more violent and more luminous and is therefore called **Hypernova** or long-term gamma ray burst. In this case, a black hole is created.

The collapse is in general **asymmetrical** and thus gives the resulting compact object a '**kick**': So there is a momentum transfer. So became a *astro-archaeological object* using the space telescope *Hubble* discovered: a stellar black hole of about six to seven solar masses, which was probably formed in a dense globular cluster. Due to the kick, it left the heap and is one of the oldest objects in the Milky Way, which has since crossed the galactic plane on a strongly eccentric orbit. Something similar can be observed with some neutron stars that wander through interstellar space at high speed.

Under the entry Penrose diagram is the representation of a spherically symmetrical (and therefore idealized) gravitational collapse, which leads to a stellar black hole. In this spacetime diagram you can follow different types of geodesics and schematically visualize the formation of an event horizon.

small note

Up was from three *End*states the speech; it does happen that the compact objects that have formed after the gravitational collapse of a star, *preliminary* Have character. It depends on the environment. If the 'final' state is fed with matter, the white dwarf, for example, can be completely torn apart in an SN Ia; if a neutron star is in a binary star system with another neutron star, sooner or later the system will merge through the emission of gravitational waves and collapse into a black hole. Only the black holes can be described as real final states - they would not even disappear through the emission of Hawking radiation, because for black holes with solar mass this takes significantly longer than the age of the universe!

These classic three and observed end states have recently been joined by a few **Alternatives**: the boson star, the fermion star, the quark star, the strange star, the gravastern, the holostar, the vacuum star - but so far there are no convincing arguments for the existence of all these modern alternatives.

Web articles

G

A-Z

up

### index

Deceleration parametersADAF

ADD scenario

ADM formalism

AdS / CFT correspondence

AGB star

Equivalence principle

Accretion

Active galactic core

Alfvén speed

Alfvén number

general theory of relativity

Alpha decay

AMR

anthropic principle

Antigravity

Antimatter

Apastron

Aperture synthesis

Aphelion

apogee

astronomy

Astronomical unit

asymptotically flat

Resolving power

Axion

AXP

Balbus-Hawley instability

Bardeen watchers

Baryogenesis

Baryons

baryonic matter

Bekenstein-Hawking entropy

observer

Beta decay

Reference system

Bianchi identities

Big bang

Big bounce

Big crunch

Big rip

Big Whimper

Birkhoff theorem

Blandford-Payne scenario

Blandford-Znajek mechanism

Blueshift

Blazar

BL Lac object

Arc minute

Arcsecond

Bosons

Boson star

Boyer-Lindquist coordinates

Bran

Brans Dicke theory

Brown dwarf

Brill waves

Bulk

Carter's constant

Casimir effect

Cauchy surface

Cepheids

Cerenkov radiation

Chandrasekhar boundary

Chaplygin gas

Chirality

Christoffel symbol

CMB

CNO cycle

Comptonization

Cosmon

C process

Deep fields

Derrick's theorem

de-sitter cosmos

DGP scenario

Diffeomorphism

differential rotation

Distance module

Dodecahedron Universe

Doppler effect

Three Kelvin radiation

Dark energy

Dark matter

Eddington-Finkelstein coordinates

Eddington luminosity

Effective temperature

Gauge theory

Einstein ring

Einstein-Rosen Bridge

Einstein tensor

Iron line

eclipse

Ecliptic

Ecpyrotic model

Electromagnetism

Electron volts

electroweak theory

Elemental charge

energy

Energy conditions

Energy-momentum tensor

Distance module

eos

eos parameters

Epicyclic

Event horizon

erg

Ergosphere

eV

Absorbance

Extra dimension

extragalactic

extrasolar

extraterrestrial

eccentricity

False color image

Fanaroff-Riley classification

Faraday rotation

Color index

Color charge

Color superconductivity

Field equations

Fermi acceleration

Fermions

Fermion star

Distant parallelism

Feynman diagram

FFO

FIDO

Flatness problem

FLRW cosmology

Escape speed

Frame dragging

f (R) -gravity

Friedmann world model

Galactic black hole candidate

Galaxy

Gamma ray burst

Gamma decay

Geodesics

Geometrized units

Geometrodynamics

Tidal forces

Tidal radius

Gluons

Degree

granulation

Gravastern

Gravity

Gravitational collapse

Gravitational cooling

Gravitational lens

Radius of gravity

Gravitational redshift

Gravitational waves

Gravitomagnetism

Graviton

GRBR

Great Unified Theories

group

WELL

GZK cutoff

Hadrons

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