### Introduction

Contents

Black holes are perhaps the most incredible objects in astronomy : they are a mass so densely packed that it even prevents light from escaping. As a consequence, a black hole is black and therefore difficult to spot in the sky. However, astronomers have developed tricky methods to find masses in the sky even when they are not shining. Based on these *indirect methods* , a large number of black hole candidates have been observed in the sky.

### Objects of general relativity

That was basically the definition of a black hole, as an astronomical observer would put it. However, there is also a stricter, mathematical definition. It is based on the general theory of relativity (ART), a theory of gravity that Albert Einstein developed almost a hundred years ago. According to this theory, gravitation is a geometrical property of space and time . Einstein showed that space and time cannot even exist independently of one another. This is how the concept of spacetime developed . You can imagine this spacetime as a mountain with mountains and valleys, ups and downs, or as one says in the ART: with**Curvatures** . A black hole is now a very special space-time, one whose curvature increases more and more from the outside in and which ultimately becomes infinite in the center of the hole. This place is called singularity in the ART . In this sense, a classic black hole is a singular solution of the Einstein field equations of the ART.

Since light now follows curved paths in a curved space-time, the so-called (zero) geodesics , the light also moves in the direction of the infinite curvature. Unfortunately, the light no longer comes out there. As a result of this property, black holes are black.

There are different types of black holes, those that rotate and those that do not. Holes with an electrical charge have even been found in theory . All of this is possible with the methods of mathematical physics. You only need ‘Einstein’s fundamental equation of the ART: the Einstein field equations. All black holes are solutions to these field equations. It is a tensorial equation that can hardly be understood with the means of school mathematics. Tensors are geometric objects that have a physical reference in the ART. In the field equations, the curvature of space-time is represented by the Riemann tensor , while the mass and energy inInsert the energy pulse tensor .

Black holes can be represented mathematically as a metric tensor or line element . If you insert this representation – this spacetime – into the Einstein equations, the equations are solved. In the words of the classic, Newtonian theory of gravitation of the 17th century, a theory of gravitational fields and gravitational forces, black holes are a certain form of a gravitational field, namely one that is able to capture the light. Newton would certainly not have understood this wording because he did not know that light has mass. But that says precisely Einstein’s famous equation *E* = *mc *^{2}, which he derived as part of the Special Theory of Relativity (SRT) in 1905. (Note: light has mass because it has energy – however, light has a *rest* mass zero, ie light has no mass in the frame of reference that moves with the light.

### Uniqueness

The singularity of black holes can be visualized very clearly: If the hole does not rotate, it is a **point mass** . More complicated is it when the hole rotates: it is a **ring mass** , or as they say in the ART, a ring singularity .

Within the framework of ART, these different black holes have been given names:

The rotating, electrically neutral form of a black hole is called the Kerr solution . The non-rotating, i.e. **static** and electrically neutral type is called the Schwarzschild solution . Historically, the structurally simpler, spherically symmetrical and static Schwarzschild solution was first found (*Karl Schwarzschild* , 1916). A Schwarzschild hole has only one property: Mass *M* . The rotating, axisymmetric, stationary generalization was discovered much later ( *Roy P. Kerr* , 1963). Kerr holes have two properties: mass *M* and angular momentum *J* . The rotation can be **parameterized** using the **Kerr parameter ***a* . *a* = *J* / *Mc* is a specific angular momentum (angular momentum / mass) and, when using geometrical units ( *G* = *c* = 1), any value from the range between -Accept *M* and + *M. *If *M* = 1 is used for further simplification , the range of numbers that defines the angular momentum of a rotating hole becomes the interval [-1; +1]. The excellent case *a* = 0 characterizes the Schwarzschild solution, with *a* less than zero there are retrograde (counter-rotating) rotations, otherwise prograde (the sense of rotation is important as soon as particles or stars circle a hole).

### At most three properties!

The metrics mentioned , Kerr and Schwarzschild geometry, are **solutions of the field equations in a vacuum** . Vacuum means that the energy pulse tensor disappears. This can be called a relativistic vacuum, which must be strictly distinguished from the quantum vacuum .

The electrically neutral black holes are space times (four-dimensional manifolds: one time dimension, three space dimensions), which are therefore completely in a vacuum.

As indicated, there is also the **electrically charged** generalization of a black hole. The electrically charged, static counterpart to the Schwarzschild solution is called the Reissner-NordstrÃ¸m solution(1918). A Reissner NordstrÃ¸m hole has the properties of mass *M* and charge *Q* .

The most common form of black holes is represented by the Kerr-Newman solution (1965). These holes have three characteristics, namely, mass *M* , angular momentum *J* and electric charge *Q* . Kerr-Newman holes have the ‘most hair’ (see no-hair theorem ).

In contrast to the Schwarzschild and Kerr geometry, Reissner-NordstrÃ¸m and Kerr-Newman space-time are **not vacuum solutions of** the Einstein field equations: the energy-momentum tensor here is the Maxwell tensorbecause a charge creates an electromagnetic field in its environment . The ART field equations that solve these charged black holes are called **Einstein-Maxwell equations** . However, all forms of electrically charged holes appear to be irrelevant in astrophysics because plasma flows in the area would neutralize this charge. The majority of astrophysicists therefore only discuss the existence of the Kerr and Schwarzschild holes. No black hole with electrical charge has been observed yet – but there are some rotating candidates; for example the super heavy hole in the center of our home galaxy .

### On the term *black hole*

Common to all black holes is the property discussed at the outset that particles and radiation that come too close to them are irretrievably lost (as one assumes): they are ‘swallowed up’. This is to be understood in the sense that the hole only absorbs the mass and angular momentum of the incident objects: it grows. However, this only happens if the test specimens really come close to the event horizon (the outer horizon). For this reason, they are called ‘ ** black** ‘ because any type of radiation (including light) that passes through this critical (zero) area gets inside black holes. Viewed from the outside, they appear black because there is no radiation flow from the region smaller than the horizon radius to the observeris achieved and absorbed. However, the event horizon is not

*a solid surface*like that of stars or planets , but rather a mathematically defined interface: the speed of escape becomes equal to the speed of vacuum

*c*, and since radiation or particles cannot move faster than light according to the special theory of relativity, they have nothing left other than to disappear into the black hole. The definition of the outer horizon is just r

_{H}= M + (M

^{2}– a

^{2})

^{1/2}, with the mass of the black hole

*M*and the rotation parameter

*a*(Extreme Kerr:

*a*=

*M*, Thornes Limit:

*a*= 0.998

*M*, Schwarzschild:

*a*= 0).

The term ‘ ** hole** ‘ comes from another special property: In the center of symmetry of space-time at

*r*= 0, the curvature becomes infinite! At this point, all physical quantities grow beyond all limits and a physical description collapses. It is an

*intrinsic singularity*(space-time

*singularity*). When black holes rotate, this point singularity inflates to a ring singularity . In any case, however, the singularity remains at the center of the hole, at

*r*= 0. To a certain extent, the rotation only changes the singularity type, not the location. The entire mass of black holes is in this singularity! It is absolutely unclear in what form the matter is in the singularity. In particular, one does not know the equation of state of this ‘singular matter’. As will be discussed later in this entry, there are indications that there may be no singularities inside black holes!

### Rotating black hole

If you approached a rotating hole from a distance, you would not feel the rotation of space-time locally because you are part of the rotation. The whole room is rotating! Only if you took a look at the fixed star sky, you would see that it rotates. Rotation can therefore only be determined relatively between the distant and local observer. The ‘space-time carousel’ turns faster and faster the closer you get to the ring singularity. An important zone that only rotating black holes are equipped with is the ergosphere . In this area, the rotation of spacetime becomes particularly violent.

Important physical processes are also associated with the ergosphere because the rotation of space-time pulls violently on particles and magnetic fields. This so-called frame-dragging effect has Penrose processes or Blandford-Znajek mechanisms result. They are important for the dynamics of material that dares to come so close to the hole. The astrophysicists assume that gigantic rays of matter – the jets – are catapulted from the rotating space-time into the vastness of space.

From what has been said so far, you can get an image of non-rotating and rotating black holes that could look like the following:

However, these images should be interpreted with a certain caution, as the discussion under the entry Kerr solution explains, because such a representation is not based on invariants. Consider this picture as information about which ‘structural ingredients’ a Schwarzschild or Kerr hole has.

### Effects on space and time for Black hole

Black holes are interesting study objects that can teach us a lot of new things about the actual nature of space and time. In particular, they are good mathematical objects for testing theories like ART. While on earth (a very flat space-time) space and time appear separately at low speeds compared to the speed of light, black holes show that they are intricately interwoven in the four-dimensional **space-time continuum** . The theory of relativity proves that at very high speeds (special relativity) or strong gravitational fields (general relativity) a geometrical object, space-time, plays the main role.

A particularly instructive thought experiment, which seems paradoxical to the earthly gaze , is that of two observers: one watches the other as he approaches a black hole. At first everything looks as usual: the one observer gets closer and closer to the area of â€‹â€‹the black hole, which the observer can confirm in the ‘infinite’, in the asymptotically flat space-time. But if the approaching observer gets into the significantly curved area of â€‹â€‹space-time around the black hole, something strange happens: the outer observer sees a **slowdown in the movement of** the free-falling observer due to the time dilation . This effect occurs in light (in the *frequency domain*) noticeable as a gravitational red shift: light loses energy due to the powerful pull of the spacetime of the hole. The free-falling observer ( FFO ), on the other hand, will approach the hole more and more from his perspective and measure a normal course of his time, the **own time** . Shortly before reaching the event horizon, the observer will no longer be able to detect any movement in the infinite: the time dilation becomes infinitely large and finite time intervals are stretched to infinitely long!

However, the free-falling observer on site will reach the horizon in finite time. If tidal forces do not tear him apart (‘spaghettize, spaghettify’, English *spaghettify*), it can even reach the singularity (should it actually be realized in nature) in *finite* time. At the latest the infinite curvature in the singularity will tear the incoming observer.

This movement will never be observed from the infinite! From a great distance, the conditions are always such that luminous, incident objects shine weaker and redder and slowly slow their movement. Finally, the object disappears into the blackness of the hole and from the gaze of the outside observer.

Ultimately, this phenomenon is an expression of **relativity**: Both observers are right in what they see, even if they see different things! There are many examples in the theory of relativity in which this relativity manifests itself: the spatial length is also relative and can appear shortened, for example at high (relativistic) speeds. This is what physicists call Lorentz contraction . The concept of particles loses its **absolute status** as well as time and length, as is manifested in the balance effect or Hawking radiation . By the way, the Hawking radiation proves that black holes are not absolutely black: the horizon can have a temperature, the so-called Hawking temperature, are assigned, which presumably results in a **thermal emission** in the manner of a Planckian radiator . However, the still hypothetical Hawking radiation is not the outflow of the (unquantized) ART itself, but only takes into account **quantum effects** on the horizon. Hawking used the semiclassical theory to derive the effect – ART plus quantum fields, but *without a quantized* gravitational field.

### mass scale ðŸ˜‹- Black hole

The mass of black holes is used to differentiate between several types, which go through different creation mechanisms and developments:

**Black mini-holes**weigh as much as elementary particles . In particular,**black holes in the TeV range**(English*TeV black holes*) have been proposed, which are about as heavy as 1000 protons, namely a TeV . However, they can only exist if there are extra dimensions and the classic Planck scale is reduced to the electroweak energy threshold (e.g. a TeV). The mini-holes are speculative, but are searched for in particle accelerators .

It has even been suggested that they be in natural form in thecosmic rays occur. But that too is speculative and has not been confirmed yet.- Primordial black holes have masses of approximately 10
^{18}g or corresponding to 10^{-15}solar masses. This corresponds approximately to the mass of an earthly mountain. The associated radius of the event horizon is only about 10^{-12}m or 1 pm and thus comes in the subatomic range. The*primordial*attribute refers to the fact that these holes may have existed in the early phases of the universe . The existence of the primordial holes is also speculative and controversial because there is no evidence from the observation, for example signatures in the cosmic background radiation . Their origin is also unclear: it could**super-critical Brill waves have**collapsed and left these tiny holes. The well-known cosmologist*Stephen Hawking*showed that such holes have to shine quickly due to quantum effects:**Hawking radiation was**named after him, the emission of which ultimately leads to the hole disappearing quickly. Therefore, the primordial holes cannot have survived into the local cosmos. - Stellar black holes have masses in the range of about 3 to 100 solar masses. Perhaps there are even holes of this type that are lighter than 3 solar masses – depending on how hard neutron stars can become. Stellar holes have been created in the gravitational collapse of massive stars. Astronomers often find them in X-ray double stars , especially microquasars are good candidates for stellar black holes. The classic mass type of the stellar black hole is the longest known historically. The astronomers assume that these star-like holes exist.
**Moderate****black holes**(in the technical language:*intermediate-mass black holes*, IMBHs) have larger masses of 100 to one million solar masses. In 2000, the discussion about the existence of black holes started based on X-ray observations of the starburst galaxy M82 with Chandra. Supercomputer simulations now support the existence of a moderately difficult hole of several hundred solar masses in the center of the young MGG 11 star cluster (*Zwart et al.*2004).

In 2002, good evidence was found that this intermediate hole type could also exist in old star clusters, the globular star clusters (objects M15 and G1). Globular clusters are ancient galactic components and are located in a spheroidal edge region of a galaxy, the galactic halo. Due to their great age, globular clusters have almost no interstellar gas left that can be collected. The middle black holes could have originated from lighter stellar black holes due to frequent*merging events occurring*in the dense globular clusters . They would have gained their current high mass of a few thousand to ten thousand solar masses through accretion .

The way in which stars move in the globular cluster around its center describes the so-called*velocity dispersion curve*, In some globular clusters, it can be explained very elegantly with massive black holes. It would also be possible for whole stars to be picked up from the central hole. Then astronomers would have the chance to indirectly deduce the existence of a massive black hole in globular clusters in the associated high-energy radiation bursts (X-ray bursts).

In the smallest galaxy types, the dwarf galaxies, some astronomers assume central black holes between 100,000 and one million solar masses. They also belong to the*intermediate-mass black holes*. Two of these candidates are the dwarf galaxies with the Seyfert core NGC 4395 (*Shih et al.*, 2003) and POX 52close (*Barth et al.*, 2003, 2004).

From a theoretical point of view, it has long been puzzling why there should not be black holes in these masses. The temptation is accordingly great to*ascribe*an existence to the*intermediate-mass black holes*. But as attractive as this hypothesis may be – the evidence for IMBHs needs to be strengthened by further observations and convincing simulations. It remains to be seen whether a new black hole mass type will be established.**Super-massive, massive or super-heavy black holes**(English*supermassive*or*massive black holes*) have even larger masses of 10^{ 6}to 10^{ 10}solar masses. The majority of astronomers are convinced that these giants are found under the holes in almost every galaxy at their center. This is particularly evident in the Active Galactic Nuclei (AGN) , whose activity cannot be explained as a key element without a ‘super hole’. This follows mathematically with the discussion of the Eddington luminosity . Also the rather inactive center of our galaxy, the Milky Way, is home to a supermassive black hole of around 3.6 million solar masses ( infrared group MPE ), which even seems to rotate. The largest masses of black holes are derived

in the huge elliptical radio galaxies that sit in the centers of gigantic galaxy clusters: 10^{10}solar masses! Extensive cosmological simulations on supercomputers, such as the*Millennium Simulation*(*Springel et al.*, Nature 435, 629, 2005), prove that the heaviest holes and the oldest stars are located in the centers of the heaviest galaxy clusters. The supermassive black holes of the galaxies M87 andCXO 0312 Fiore P3 . The powerful radio galaxy Cygnus A is located just below . This is shown by astronomical observation.

### How to spot a black hole

Black holes can be demonstrated astronomically by their extreme or exotic effects on their immediate surroundings. Meanwhile, numerous astronomical observations attest that black holes must exist. It is advisable to assign a nomenclature to the different detection methods that is related to the respective effect ( *A. MÃ¼ller* : PhD thesis 2004; Proceeding Dubrovnik Summer School 2007):

**Kinematic verification**: Stars can circle around black holes on stable Kepler orbits. From the speed of this movement follows the mass of the hole that the star orbits at a certain distance (see also Kepler laws ). Black holes follow in many cases if the derived central mass is high, dark and compact. In this context, these astronomers speak of the**MDO**, the*massive dark object*.

The mass of many high-mass black holes also follows kinematically from the velocity dispersion with the**M-Ïƒ relation**(description of this relationship belowsuper-massive black holes ).

A method called reverberation mapping can also be called a kinematic method. Astronomers estimate the masses (precise:*virial masses*) of black holes by determining the Doppler speeds and the distance of the luminous clouds of matter from the center of rotation.**eruptive verification**: Stars that come too close to the black hole and reach the tidal radius can be completely torn apart in a spectacular manner with the appropriate mass and radius. This*stellar tidal disruption*due to strong tension and compression is observed as an X-ray flare with a characteristic signature. Such phenomena are of particular importance for ‘sleeping black holes’ in inactive galaxy centers, which, due to a lack of surrounding material, can hardly accentuate them.

But also the gamma ray bursts (including hypernovae) can be seen in many cases as eruptive indicators of stellar black holes that have just been formed ( a neutron star is usually formed in supernovae ).**Accurate verification**: If there is sufficient interstellar gas in the vicinity of black holes, it is collected by the hole. This process is called accretion . The gas heats up to a hot, ionized and magnetized accretion flow. The heating takes place on the one hand hydrodynamically via turbulence and dissipative viscosity, i.e. in principle the friction of the plasma particles in the viscous flow, but on the other hand also magnetohydrodynamically via magnetic turbulence (see MRI) and reconnection, i.e. the destruction of magnetic fields of opposite polarity. The energy stored in the fields is thus transferred to the plasma in the form of kinetic energy. Radiation processes (brake radiation, Comptonization , synchrotron radiation ) also play a major role in heating and cooling the accretion flow. Ultimately, a large part of the flowing plasma is collected by the black hole, enriches it with even more mass and thus enlarges it. The gas glows with powerful and variable emissions in all spectral ranges and ensures the typical enormous luminosity according to the**AGN paradigm**active galaxy nuclei. This activity reveals the existence of super-massive black holes in the galaxy centers because they follow directly from the Eddington argument .**Spectro-relativistic verification**: spectra of luminous matter in the vicinity of black holes are strongly deformed by relativistic effects such as beaming , lens effects and gravitational redshift . This applies in particular to spectral lines, especially in the area of â€‹â€‹X-rays, for example in the iron line (Fe KÎ±). Such relativistic spectra and spectral lines can serve as a diagnostic tool to detect a black hole and to study its surroundings. The astronomers can deduce some parameters of the black hole from the spectra.**Obscurative verification**: The gravitational redshift causes a blackening of the boundary area around the black hole around the outer horizon, and not only on the horizon itself. The relativistic redshift factor (relativistic generalized Doppler factor, g factor) influences**all forms of electromagnetic radiation**in the vicinity of black holes. Because within the framework of the theory it is known that the g-factor is used in high power when evaluating the radiation flow. This ensures strong suppression of radiation emissions near the horizon. Even the current alternatives to the classical black hole ( Gravasterne and Holosterne- more on that in a moment) are very dark, not absolutely black, but almost. Therefore, a pronounced dark zone around the compact object must also be observable. Astronomers try this ‘**Big Black spot**‘ (Engl.*Great Black Spot*, GBS, see PhD A. MÃ¼ller) to measure. On the celestial sphere, however, the apparent diameter of the black spot of candidate objects for black holes is almost tiny and is in the range of micro-arc seconds (millionths of an arc second; for comparison: the apparent diameter of the full moon is approximately 1,800 arc seconds). This form of black hole diagnostics is still a dream of the future because of the spatial resolutionmodern telescopes are not yet sufficient for this. The earliest success is promised by radio astronomy, which uses VLBI to achieve the greatest resolution in astronomy. The forecast is that within the next five to ten years the black spot could be radio-astronomically displayed in the millimeter wave range (*Krichbaum et al.*, MPIfR Bonn, ePrints under astro-ph / 0411487 , astro-ph / 0610712 and astro-ph / 0611288 ). It is therefore to be expected that telescopes will soon be able todetect black holes by swiveling over these dark areas . Simulations using ray tracing already show this effect in the computer laboratory!*directly***aberrative verification**: The compact mass of a black hole can cause**lens effects**and deflect or concentrate radiation from other cosmic objects. In this way, compact, dark masses can be derived indirectly, especially the larger, super-mass black holes. But stellar black holes could also serve as microlensesbe diagnosed. It is particularly interesting that the orbital shape of an encircling body, which in itself is circular or elliptical, is extremely relativistically distorted. Evidence of observation of exotic orbital shapes would therefore reveal black holes and even allow the limitation of some typical parameters such as orbital radius, inclination of the orbital plane and rotation of the hole (can also be read in detail in my doctoral thesis, p.38f).**Temporal verification**: This detection method takes advantage of the effect that the measure of time is stretched near black holes (*time dilation*). Time-varying phenomena at the hole, for example in the accretion disk or a star circling around the hole, are therefore subject to this effect. From the analysis of light curves , the astronomer could determine that a time-varying process was ‘temporally distorted’ by the presence of the hole (*Cunningham*&*Bardeen*1973). This would be very easy to recognize if the astronomer knew what the temporal variation should look like – namely in the rest system. The properties of the hole can also be derived from the investigation of time-dependent phenomena in the vicinity of black holes, which is the basic idea of â€‹â€‹these temporal methods.

The spatially us **cosmic nearest-black hole** is located in the X-ray binary XTE J1118 to + 480 . This galactic black hole candidate can be found in the constellation *Ursa Major* (German: *Great Bear* , actually *Great Bear* ) and has a distance of 1800 parsec or 5870 light years . It sits in the galactic halo of the Milky Way, that is the spherical border region of our galaxy where the globular clusters frolic. The black hole in this binary system weighs about eight solar masses ( *McClintock et al.* 2004, astro-ph / 0403251).

### But no Black hole?

In 2001 physicists theoretically found new alternatives to the classic, singular black holes alongside boson and fermion stars . These new spacetime have no event horizon, and one of them does not need a singularity and is therefore **regular** . The first proposal was christened by the discoverers *P. Mazur* & *E. Mottola *Gravastern ( *Mazur* & *Mottola* 2001, gr-qc / 0109035 ). The outermost part of the gravity star corresponds to the Schwarzschild solution, followed by a thin shell of an ultra-relativistic plasma, which is caused by an inner ‘bubble’ of dark energyis stabilized. Grava stars are static; no rotating generalization has yet been found.

The second proposal, which is an alternative to the classic black hole, is called holostern ( *M. Petri* 2003, gr-qc / 0306063 and gr-qc / 0306066 ). Indeed, there are a number of similarities between gravaster stars and holostars: the most important thing in common is that both types of solutions have no event horizon!

The inside of the holostar can be understood as radial stringsensure anisotropic pressure inside (however, interpretation with strings is not mandatory). For example, where the horizon is in the classic Schwarzschild hole, the holoster has a membrane, which probably also consists of particles. However, this membrane has zero thickness.

The two new solutions have the same limitation as the classic Schwarzschild geometry: no rotation. However, rotation is not only suggested by all possible cosmic, rotating objects, but is in particular a **vital prerequisite** for generating the observed jets magnetohydrodynamically in an ergosphere (see above, also described in detail under Blandford-Znajek mechanism and Penrose process ). So long as no generalization to the rotating gravaster or the rotating holoster is found within the framework of the theory, the **Kerr geometry** must be regarded as the astrophysically relevant space-time, even if it is singular inside. However, this does not mean that alternatives should be left out – on the contrary. Researching the new regular spacetime is an exciting, current area of â€‹â€‹research.

### Thermodynamics of black holes

Black holes can also be treated as part of thermodynamics . One finds properties of the holes that have an analogy to thermodynamic quantities. These include the Hawking temperature and the Bekenstein-Hawking entropy . The derived numerical value of this entropy stimulates discussion, because *Bekenstein* already showed in 1973 that black holes have enormous entropies. Even a stellar black hole from a solar mass has an entropy of 10 ^{77} k _{B} (k _{B}is the Boltzmann constant). This gigantic value lies far above the entropy of a typical star, which must have been the forerunner of such a black hole. This problem is known as the **entropy paradox** ( *information ***paradox** ). Gravastars solve this paradox because they have much smaller entropies. It only scales linearly with the mass of the thin material shell that envelops the gravaster.

According to current knowledge, string theories also solve the entropy paradox. They even go a little further: *Samir Mathur* ( *Mathur* 2004, hep-th / 0401115 ) argues that the event horizon is a conglomerate of strings andBranen cover up. He calls this structure *fuzzball* (German: ‘lint ball’). It still contains information about the precursor from which the hole originated. The Hawking radiation can now absorb and radiate this information. This means that not everything in the hole would be lost if this string scenario were correct. Black holes would have ‘a few more hairs’!

### The singularity question on black holes

The figure above is a schematic comparison between classic and modern spacetime that looks like a black hole from the outside, but differs greatly on the inside ( large version ). To date, no one can say which view is correct! Every theory on which the proposals are based has its advantages and disadvantages. The ART is a theory that has proven itself, but it is not clear whether physicists are already moving beyond their scope if they want to describe the event horizon and the inside of a black hole (quantum effects!). String theories are a good candidate for a unified oneTheory. Nevertheless, they still owe the physicists proof that they actually describe nature. In this respect, all string theory statements are subject to a certain reservation. Holostars are an attractive, theoretical alternative. Their interior can even be reconciled with string theories. Also the gravity stars in quantum gravity from *Mazur & Mottola*are attractive. However, their external metric does not differ from the classic Schwarzschild case of ART. In view of the strong shift in the gravitational red, it seems questionable whether it can ever be decided by astronomical observation whether it is a black hole, a holoster, a gravaster or a fuzzball. The current state of the theory outlines a hopeless situation: You can literally see black!

### Clarification with gravitational waves or loops?

There are now signs of a possible way out of the dilemma: It is true that the gravitational redshift makes it difficult to distinguish – but only if one observes with electromagnetic waves. It has recently been shown that the event horizon and hole spin could be detected using gravitational waves ( *Berti & Cardoso* 2006, gr-qc / 0605101 ). Experimental gravitational wave research is in full swing, so there is hope that exciting news will soon be available. If this succeeds, it could be called the *gravitational wave-induced verification method of* black holes ( *MÃ¼ller* 2004).

Loop quantum gravity also has positive developments : various authors have shown that curvature singularities can be avoided through loop effects ( *Bojowald et al.* 2005, *Goswami et al.* 2006).

However, the **question of singularities** has not yet been solved: Are singularities a part of nature or are they an artifact of an inadequate, mathematical description?

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