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Enabling JavaScript in your browser will allow you to experience all the features of our site. Learn how to enable JavaScript on your browser. These proceedings collect the selected contributions of participants of the First Karl Schwarzschild Meeting on Gravitational Physics, held in Frankfurt, Germany to celebrate the th anniversary of Schwarzschild's birth. They are grouped into 4 main themes: I. Other Topics in Contemporary Gravitation. In addition to plenary talks from leading researchers, a special focus on young talent was provided, a feature underlined by the Springer Prize for the best student and junior presentations.

Siegel and Riccardo Ciolfi. See All Customer Reviews. Shop Books. Add to Wishlist. USD Sign in to Purchase Instantly. Overview These proceedings collect the selected contributions of participants of the First Karl Schwarzschild Meeting on Gravitational Physics, held in Frankfurt, Germany to celebrate the th anniversary of Schwarzschild's birth.

Product Details Table of Contents. Roberto Casadio. This interdisciplinary conference brings together researchers in computer science, artificial intelligence, artificial life, control, robotics, neurosciences, ethology, evolutionary biology and related fields in order to further our understanding of the behaviours and underlying mechanisms that allow natural and artificial animals so-called animats to adapt and survive in uncertain environments. The symposium brings together leading experimenters, theorists and method developers from the field of neuroscience to exchange fundamental questions.

The aim is to understand the functioning and logistical challenges of nerve cells from the ground up. It was its goal to connect experienced Science communicators with scientists to exchange knowledge and expand networks. A complete extension had already been found by Martin Kruskal , who was urged to publish it. These results came at the beginning of the golden age of general relativity , which was marked by general relativity and black holes becoming mainstream subjects of research. This process was helped by the discovery of pulsars by Jocelyn Bell Burnell in , [42] [43] which, by , were shown to be rapidly rotating neutron stars.

In this period more general black hole solutions were found. In , Roy Kerr found the exact solution for a rotating black hole. Two years later, Ezra Newman found the axisymmetric solution for a black hole that is both rotating and electrically charged. At first, it was suspected that the strange features of the black hole solutions were pathological artifacts from the symmetry conditions imposed, and that the singularities would not appear in generic situations. This view was held in particular by Vladimir Belinsky , Isaak Khalatnikov , and Evgeny Lifshitz , who tried to prove that no singularities appear in generic solutions.

However, in the late s Roger Penrose [51] and Stephen Hawking used global techniques to prove that singularities appear generically. Work by James Bardeen , Jacob Bekenstein , Carter, and Hawking in the early s led to the formulation of black hole thermodynamics. The analogy was completed when Hawking, in , showed that quantum field theory predicts that black holes should radiate like a black body with a temperature proportional to the surface gravity of the black hole.

John Michell used the term "dark star", [55] and in the early 20th century, physicists used the term "gravitationally collapsed object". Science writer Marcia Bartusiak traces the term "black hole" to physicist Robert H. Dicke , who in the early s reportedly compared the phenomenon to the Black Hole of Calcutta , notorious as a prison where people entered but never left alive. The term "black hole" was used in print by Life and Science News magazines in , [56] and by science journalist Ann Ewing in her article " 'Black Holes' in Space", dated 18 January , which was a report on a meeting of the American Association for the Advancement of Science held in Cleveland, Ohio.

In December , a student reportedly suggested the phrase "black hole" at a lecture by John Wheeler ; [57] Wheeler adopted the term for its brevity and "advertising value", and it quickly caught on, [59] leading some to credit Wheeler with coining the phrase. The no-hair conjecture postulates that, once it achieves a stable condition after formation, a black hole has only three independent physical properties: mass , charge , and angular momentum ; the black hole is otherwise featureless. If the conjecture is true, any two black holes that share the same values for these properties, or parameters, are indistinguishable from one another.

The degree to which the conjecture is true for real black holes under the laws of modern physics, is currently an unsolved problem. These properties are special because they are visible from outside a black hole. For example, a charged black hole repels other like charges just like any other charged object.

Similarly, the total mass inside a sphere containing a black hole can be found by using the gravitational analog of Gauss's law , the ADM mass , far away from the black hole. When an object falls into a black hole, any information about the shape of the object or distribution of charge on it is evenly distributed along the horizon of the black hole, and is lost to outside observers. The behavior of the horizon in this situation is a dissipative system that is closely analogous to that of a conductive stretchy membrane with friction and electrical resistance —the membrane paradigm.

Because a black hole eventually achieves a stable state with only three parameters, there is no way to avoid losing information about the initial conditions: the gravitational and electric fields of a black hole give very little information about what went in. The information that is lost includes every quantity that cannot be measured far away from the black hole horizon, including approximately conserved quantum numbers such as the total baryon number and lepton number.

This behavior is so puzzling that it has been called the black hole information loss paradox. The simplest static black holes have mass but neither electric charge nor angular momentum.

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These black holes are often referred to as Schwarzschild black holes after Karl Schwarzschild who discovered this solution in The popular notion of a black hole "sucking in everything" in its surroundings is therefore only correct near a black hole's horizon; far away, the external gravitational field is identical to that of any other body of the same mass.

Solutions describing more general black holes also exist. The most general stationary black hole solution known is the Kerr—Newman metric , which describes a black hole with both charge and angular momentum. While the mass of a black hole can take any positive value, the charge and angular momentum are constrained by the mass. Black holes with the minimum possible mass satisfying this inequality are called extremal. Solutions of Einstein's equations that violate this inequality exist, but they do not possess an event horizon.

These solutions have so-called naked singularities that can be observed from the outside, and hence are deemed unphysical. The cosmic censorship hypothesis rules out the formation of such singularities, when they are created through the gravitational collapse of realistic matter. Due to the relatively large strength of the electromagnetic force , black holes forming from the collapse of stars are expected to retain the nearly neutral charge of the star.

Rotation, however, is expected to be a universal feature of compact astrophysical objects. That uncharged limit is [70]. Black holes are commonly classified according to their mass, independent of angular momentum, J. The size of a black hole, as determined by the radius of the event horizon, or Schwarzschild radius , is proportional to the mass, M , through. The defining feature of a black hole is the appearance of an event horizon—a boundary in spacetime through which matter and light can only pass inward towards the mass of the black hole.

Nothing, not even light, can escape from inside the event horizon. The event horizon is referred to as such because if an event occurs within the boundary, information from that event cannot reach an outside observer, making it impossible to determine if such an event occurred. As predicted by general relativity, the presence of a mass deforms spacetime in such a way that the paths taken by particles bend towards the mass. To a distant observer, clocks near a black hole would appear to tick more slowly than those further away from the black hole. Typically this process happens very rapidly with an object disappearing from view within less than a second.

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On the other hand, indestructible observers falling into a black hole do not notice any of these effects as they cross the event horizon. According to their own clocks, which appear to them to tick normally, they cross the event horizon after a finite time without noting any singular behaviour; in classical general relativity, it is impossible to determine the location of the event horizon from local observations, due to Einstein's equivalence principle. The shape of the event horizon of a black hole is always approximately spherical. At the center of a black hole, as described by general relativity, may lie a gravitational singularity , a region where the spacetime curvature becomes infinite.

It can also be shown that the singular region contains all the mass of the black hole solution. Observers falling into a Schwarzschild black hole i. They can prolong the experience by accelerating away to slow their descent, but only up to a limit. Before that happens, they will have been torn apart by the growing tidal forces in a process sometimes referred to as spaghettification or the "noodle effect".

Extending these solutions as far as possible reveals the hypothetical possibility of exiting the black hole into a different spacetime with the black hole acting as a wormhole. The appearance of singularities in general relativity is commonly perceived as signaling the breakdown of the theory. To date, it has not been possible to combine quantum and gravitational effects into a single theory, although there exist attempts to formulate such a theory of quantum gravity.

It is generally expected that such a theory will not feature any singularities. The photon sphere is a spherical boundary of zero thickness in which photons that move on tangents to that sphere would be trapped in a circular orbit about the black hole. For non-rotating black holes, the photon sphere has a radius 1. Their orbits would be dynamically unstable , hence any small perturbation, such as a particle of infalling matter, would cause an instability that would grow over time, either setting the photon on an outward trajectory causing it to escape the black hole, or on an inward spiral where it would eventually cross the event horizon.

While light can still escape from the photon sphere, any light that crosses the photon sphere on an inbound trajectory will be captured by the black hole. Hence any light that reaches an outside observer from the photon sphere must have been emitted by objects between the photon sphere and the event horizon. Rotating black holes are surrounded by a region of spacetime in which it is impossible to stand still, called the ergosphere. This is the result of a process known as frame-dragging ; general relativity predicts that any rotating mass will tend to slightly "drag" along the spacetime immediately surrounding it.

Any object near the rotating mass will tend to start moving in the direction of rotation.


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For a rotating black hole, this effect is so strong near the event horizon that an object would have to move faster than the speed of light in the opposite direction to just stand still. The ergosphere of a black hole is a volume whose inner boundary is the black hole's oblate spheroid event horizon and a pumpkin-shaped outer boundary, which coincides with the event horizon at the poles but noticeably wider around the equator.

The outer boundary is sometimes called the ergosurface. Objects and radiation can escape normally from the ergosphere. Through the Penrose process , objects can emerge from the ergosphere with more energy than they entered. This energy is taken from the rotational energy of the black hole causing the latter to slow. In Newtonian gravity , test particles can stably orbit at arbitrary distances from a central object.

In general relativity , however, there exists an innermost stable circular orbit often called the ISCO , inside of which, any infinitesimal perturbations to a circular orbit will lead to inspiral into the black hole. Given the bizarre character of black holes, it was long questioned whether such objects could actually exist in nature or whether they were merely pathological solutions to Einstein's equations. Einstein himself wrongly thought that black holes would not form, because he held that the angular momentum of collapsing particles would stabilize their motion at some radius.

However, a minority of relativists continued to contend that black holes were physical objects, [] and by the end of the s, they had persuaded the majority of researchers in the field that there is no obstacle to the formation of an event horizon. Penrose demonstrated that once an event horizon forms, general relativity without quantum mechanics requires that a singularity will form within.

Gravitational collapse occurs when an object's internal pressure is insufficient to resist the object's own gravity. For stars this usually occurs either because a star has too little "fuel" left to maintain its temperature through stellar nucleosynthesis , or because a star that would have been stable receives extra matter in a way that does not raise its core temperature. In either case the star's temperature is no longer high enough to prevent it from collapsing under its own weight.

The result is one of the various types of compact star. Which type forms depends on the mass of the remnant of the original star left after the outer layers have been blown away. Such explosions and pulsations lead to planetary nebula. No known mechanism except possibly quark degeneracy pressure, see quark star is powerful enough to stop the implosion and the object will inevitably collapse to form a black hole. The gravitational collapse of heavy stars is assumed to be responsible for the formation of stellar mass black holes.

These black holes could be the seeds of the supermassive black holes found in the centers of most galaxies. While most of the energy released during gravitational collapse is emitted very quickly, an outside observer does not actually see the end of this process. Even though the collapse takes a finite amount of time from the reference frame of infalling matter, a distant observer would see the infalling material slow and halt just above the event horizon, due to gravitational time dilation.

Light from the collapsing material takes longer and longer to reach the observer, with the light emitted just before the event horizon forms delayed an infinite amount of time. Thus the external observer never sees the formation of the event horizon; instead, the collapsing material seems to become dimmer and increasingly red-shifted, eventually fading away.

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Gravitational collapse requires great density. In the current epoch of the universe these high densities are only found in stars, but in the early universe shortly after the Big Bang densities were much greater, possibly allowing for the creation of black holes. High density alone is not enough to allow black hole formation since a uniform mass distribution will not allow the mass to bunch up.

In order for primordial black holes to have formed in such a dense medium, there must have been initial density perturbations that could then grow under their own gravity. Different models for the early universe vary widely in their predictions of the scale of these fluctuations. Various models predict the creation of primordial black holes ranging in size from a Planck mass to hundreds of thousands of solar masses. Despite the early universe being extremely dense —far denser than is usually required to form a black hole—it did not re-collapse into a black hole during the Big Bang.

Models for gravitational collapse of objects of relatively constant size, such as stars , do not necessarily apply in the same way to rapidly expanding space such as the Big Bang. Gravitational collapse is not the only process that could create black holes. In principle, black holes could be formed in high-energy collisions that achieve sufficient density. As of , no such events have been detected, either directly or indirectly as a deficiency of the mass balance in particle accelerator experiments.

These theories are very speculative, and the creation of black holes in these processes is deemed unlikely by many specialists. Once a black hole has formed, it can continue to grow by absorbing additional matter. Any black hole will continually absorb gas and interstellar dust from its surroundings. This is the primary process through which supermassive black holes seem to have grown. This is thought to have been important, especially in the early growth of supermassive black holes, which could have formed from the aggregation of many smaller objects.

By applying quantum field theory to a static black hole background, he determined that a black hole should emit particles that display a perfect black body spectrum. Since Hawking's publication, many others have verified the result through various approaches. Hence, large black holes emit less radiation than small black holes.

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Stellar-mass or larger black holes receive more mass from the cosmic microwave background than they emit through Hawking radiation and thus will grow instead of shrinking. Such a black hole would have a diameter of less than a tenth of a millimeter. If a black hole is very small, the radiation effects are expected to become very strong.

For such a small black hole, quantum gravitation effects are expected to play an important role and could hypothetically make such a small black hole stable, although current developments in quantum gravity do not indicate this is the case. The Hawking radiation for an astrophysical black hole is predicted to be very weak and would thus be exceedingly difficult to detect from Earth.

A possible exception, however, is the burst of gamma rays emitted in the last stage of the evaporation of primordial black holes. Searches for such flashes have proven unsuccessful and provide stringent limits on the possibility of existence of low mass primordial black holes. If black holes evaporate via Hawking radiation , a solar mass black hole will evaporate beginning once the temperature of the cosmic microwave background drops below that of the black hole over a period of 10 64 years.

Even these would evaporate over a timescale of up to 10 years. By their very nature, black holes do not directly emit any electromagnetic radiation other than the hypothetical Hawking radiation , so astrophysicists searching for black holes must generally rely on indirect observations. For example, a black hole's existence can sometimes be inferred by observing its gravitational interactions with its surroundings. On 10 April an image was released of a black hole, which is seen in magnified fashion because the light paths near the event horizon are highly bent. The dark shadow in the middle results from light paths absorbed by the black hole.

The image is in false color, as the detected light halo in this image is not in the visible spectrum, but radio waves. The existence of magnetic fields had been predicted by theoretical studies of black holes. On 14 September the LIGO gravitational wave observatory made the first-ever successful direct observation of gravitational waves. The objects must therefore have been extremely compact, leaving black holes as the most plausible interpretation.

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More importantly, the signal observed by LIGO also included the start of the post-merger ringdown , the signal produced as the newly formed compact object settles down to a stationary state. Arguably, the ringdown is the most direct way of observing a black hole. From these it is possible to infer the mass and angular momentum of the final object, which match independent predictions from numerical simulations of the merger.

Hence, observation of this mode confirms the presence of a photon sphere, however it cannot exclude possible exotic alternatives to black holes that are compact enough to have a photon sphere. The observation also provides the first observational evidence for the existence of stellar-mass black hole binaries. Furthermore, it is the first observational evidence of stellar-mass black holes weighing 25 solar masses or more. On 15 June , a second detection of a gravitational wave event from colliding black holes was announced, [] and other gravitational wave events have since been observed.

The proper motions of stars near the center of our own Milky Way provide strong observational evidence that these stars are orbiting a supermassive black hole. By fitting their motions to Keplerian orbits , the astronomers were able to infer, in , that a 2. From the orbital data, astronomers were able to refine the calculations of the mass to 4.

Due to conservation of angular momentum , [] gas falling into the gravitational well created by a massive object will typically form a disc-like structure around the object. Artists' impressions such as the accompanying representation of a black hole with corona commonly depict the black hole as if it were a flat-space body hiding the part of the disc just behind it, but in reality gravitational lensing would greatly distort the image of the accretion disk. Within such a disc, friction would cause angular momentum to be transported outward, allowing matter to fall further inward, thus releasing potential energy and increasing the temperature of the gas.

When the accreting object is a neutron star or a black hole, the gas in the inner accretion disc orbits at very high speeds because of its proximity to the compact object.

The resulting friction is so significant that it heats the inner disc to temperatures at which it emits vast amounts of electromagnetic radiation mainly X-rays. These bright X-ray sources may be detected by telescopes. In many cases, accretion discs are accompanied by relativistic jets that are emitted along the poles, which carry away much of the energy.

The mechanism for the creation of these jets is currently not well understood, in part due to insufficient data. As such, many of the universe's more energetic phenomena have been attributed to the accretion of matter on black holes. In particular, active galactic nuclei and quasars are believed to be the accretion discs of supermassive black holes.

In November the first direct observation of a quasar accretion disk around a supermassive black hole was reported. X-ray binaries are binary star systems that emit a majority of their radiation in the X-ray part of the spectrum. These X-ray emissions are generally thought to result when one of the stars compact object accretes matter from another regular star. The presence of an ordinary star in such a system provides an opportunity for studying the central object and to determine if it might be a black hole.

If such a system emits signals that can be directly traced back to the compact object, it cannot be a black hole. The absence of such a signal does, however, not exclude the possibility that the compact object is a neutron star. By studying the companion star it is often possible to obtain the orbital parameters of the system and to obtain an estimate for the mass of the compact object. If this is much larger than the Tolman—Oppenheimer—Volkoff limit that is, the maximum mass a neutron star can have before it collapses then the object cannot be a neutron star and is generally expected to be a black hole.

Currently, better candidates for black holes are found in a class of X-ray binaries called soft X-ray transients. In this class of system, the companion star is of relatively low mass allowing for more accurate estimates of the black hole mass. Moreover, these systems actively emit X-rays for only several months once every 10—50 years. During the period of low X-ray emission called quiescence , the accretion disc is extremely faint allowing detailed observation of the companion star during this period.

One of the best such candidates is V Cygni. The faintness of the accretion disc of an X-ray binary during quiescence is suspected to be caused by the flow of mass entering a mode called an advection-dominated accretion flow ADAF. In this mode, almost all the energy generated by friction in the disc is swept along with the flow instead of radiated away. If this model is correct, then it forms strong qualitative evidence for the presence of an event horizon, [] since if the object at the center of the disc had a solid surface, it would emit large amounts of radiation as the highly energetic gas hits the surface, [ clarification needed ] an effect that is observed for neutron stars in a similar state.

The X-ray emissions from accretion disks sometimes flicker at certain frequencies. These signals are called quasi-periodic oscillations and are thought to be caused by material moving along the inner edge of the accretion disk the innermost stable circular orbit. As such their frequency is linked to the mass of the compact object.

They can thus be used as an alternative way to determine the mass of candidate black holes. Astronomers use the term " active galaxy " to describe galaxies with unusual characteristics, such as unusual spectral line emission and very strong radio emission. Theoretical and observational studies have shown that the activity in these active galactic nuclei AGN may be explained by the presence of supermassive black holes , which can be millions of times more massive than stellar ones.

The models of these AGN consist of a central black hole that may be millions or billions of times more massive than the Sun ; a disk of gas and dust called an accretion disk; and two jets perpendicular to the accretion disk. Although supermassive black holes are expected to be found in most AGN, only some galaxies' nuclei have been more carefully studied in attempts to both identify and measure the actual masses of the central supermassive black hole candidates.

It is now widely accepted that the center of nearly every galaxy, not just active ones, contains a supermassive black hole. Another way that the black hole nature of an object may be tested in the future is through observation of effects caused by a strong gravitational field in their vicinity.

One such effect is gravitational lensing : The deformation of spacetime around a massive object causes light rays to be deflected much as light passing through an optic lens. Observations have been made of weak gravitational lensing, in which light rays are deflected by only a few arcseconds. However, it has never been directly observed for a black hole. The evidence for stellar black holes strongly relies on the existence of an upper limit for the mass of a neutron star.

The size of this limit heavily depends on the assumptions made about the properties of dense matter. New exotic phases of matter could push up this bound. However, it can be shown from arguments in general relativity that any such object will have a maximum mass.


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For example, a supermassive black hole could be modelled by a large cluster of very dark objects. However, such alternatives are typically not stable enough to explain the supermassive black hole candidates. The evidence for the existence of stellar and supermassive black holes implies that in order for black holes to not form, general relativity must fail as a theory of gravity, perhaps due to the onset of quantum mechanical corrections. A much anticipated feature of a theory of quantum gravity is that it will not feature singularities or event horizons and thus black holes would not be real artifacts.

A few theoretical objects have been conjectured to match observations of astronomical black hole candidates identically or near-identically, but which function via a different mechanism. These include the gravastar , the black star , [] and the dark-energy star. In , Hawking showed under general conditions [Note 5] that the total area of the event horizons of any collection of classical black holes can never decrease, even if they collide and merge.

As with classical objects at absolute zero temperature, it was assumed that black holes had zero entropy. If this were the case, the second law of thermodynamics would be violated by entropy-laden matter entering a black hole, resulting in a decrease of the total entropy of the universe.

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Therefore, Bekenstein proposed that a black hole should have an entropy, and that it should be proportional to its horizon area. The link with the laws of thermodynamics was further strengthened by Hawking's discovery that quantum field theory predicts that a black hole radiates blackbody radiation at a constant temperature. This seemingly causes a violation of the second law of black hole mechanics, since the radiation will carry away energy from the black hole causing it to shrink. The radiation, however also carries away entropy, and it can be proven under general assumptions that the sum of the entropy of the matter surrounding a black hole and one quarter of the area of the horizon as measured in Planck units is in fact always increasing.

This allows the formulation of the first law of black hole mechanics as an analogue of the first law of thermodynamics , with the mass acting as energy, the surface gravity as temperature and the area as entropy. One puzzling feature is that the entropy of a black hole scales with its area rather than with its volume, since entropy is normally an extensive quantity that scales linearly with the volume of the system.

This odd property led Gerard 't Hooft and Leonard Susskind to propose the holographic principle , which suggests that anything that happens in a volume of spacetime can be described by data on the boundary of that volume. Although general relativity can be used to perform a semi-classical calculation of black hole entropy, this situation is theoretically unsatisfying. In statistical mechanics , entropy is understood as counting the number of microscopic configurations of a system that have the same macroscopic qualities such as mass , charge , pressure , etc. Without a satisfactory theory of quantum gravity , one cannot perform such a computation for black holes.

Some progress has been made in various approaches to quantum gravity.