Scientists have discovered the two biggest black holes ever observed, each with a mass billions of times greater than the Sun’s, according to a study published overnight. The two giants are located in the heart of a pair of galaxies several hundred million light years from Earth, the study was published in the scientific journal Nature.
Each black hole is estimated to have a mass about 10 billion times greater than the sun, dwarfing the previously largest-known black hole, which has a mass of 6.3 billion suns. The University of California, Berkeley, team led by Nicholas McConnell and Chung-Pei Ma said one black hole is located in NGC 3842, the brightest of a cluster of galaxies about 320 million light years from Earth. The second hole is of “comparable or greater mass” and is located in NGC 4889, the brightest galaxy in the Coma cluster, about 335 million light years away.
“These two black holes are significantly more massive than predicted,” the astronomers wrote.
The researchers said their calculations suggest that different evolutionary processes influence the growth of the largest galaxies and their black holes than in smaller galaxies. Astronomers have long supposed that since the universe began it has harboured black holes with a mass the size of the two newly found giants. These cosmic gluttons grow in tandem with their galaxies, slurping up gases, planets and stars ::::
“There is a symbiotic relationship between black holes and their galaxies that has existed since the dawn of time,” Kevin Schawinski, a Yale astronomer said in a June study.
Observations with the Hubble Space Telescope over the years have shown that such monster Black Holes seem to inhabit the centers of all galaxies, the bigger the galaxy, the bigger the black hole. Researchers say that this new work could shed light on the role these black holes play in the formation of galaxies.
“Measurements of these massive black holes will help us understand how their host galaxies were assembled, and how the holes achieved such monstrous mass,” McConnell said.
McConnell and Chung-Pei Ma, led a team of astronomers who used telescopes in Hawaii, Texas and outer space to weigh the Black Holes in the centers of galaxies. The researchers measured the speed of stars travelling around the Black Holes; the faster the stars travel, the more gravity and thus mass is needed to keep the stars from flying away.
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole.
Around a black hole there is a mathematically defined surface called an event horizon that marks the point of no return. It is called “black” because it absorbs all the light that hits the horizon, reflecting nothing, just like a perfect black body in thermodynamics.
Quantum mechanics predicts that black holes emit radiation like a black body with a finite temperature. This temperature is inversely proportional to the mass of the black hole, making it difficult to observe this radiation for black holes of stellar mass or greater.
The idea of a body so massive that even light could not escape was first put forward by geologist John Michell in a letter written to Henry Cavendish in 1783 of the Royal Society:
If the semi-diameter of a sphere of the same density as the Sun were to exceed that of the Sun in the proportion of 500 to 1, a body falling from an infinite height towards it would have acquired at its surface greater velocity than that of light, and consequently supposing light to be attracted by the same force in proportion to its vis inertiae, with other bodies, all light emitted from such a body would be made to return towards it by its own proper gravity.
In 1796, mathematician Pierre-Simon Laplace promoted the same idea in the first and second editions of his book Exposition du système du Monde (it was removed from later editions). Such “dark stars” were largely ignored in the nineteenth century, since it was not understood how a massless wave such as light could be influenced by gravity.
Related: Amusingly, while scientists are discovering Dark Energy in far off galaxies, in our own backyard Black Holes remain undiscovered, Hypothesis and Theories aren’t discoveries . . .
Objects whose gravity field is too strong for light to escape were first considered in the 18th century by John Michell and Pierre-Simon Laplace. The first modern solution of general relativity that would characterize a black hole was found by Karl Schwarzschild in 1916, although its interpretation as a region of space from which nothing can escape was not fully appreciated for another four decades.
Long considered a mathematical curiosity, it was during the 1960s that theoretical work showed black holes were a generic prediction of general relativity. The discovery of neutron stars sparked interest in gravitationally collapsed compact objects as a possible astrophysical reality.
Despite its invisible interior, the presence of a black hole can be inferred through its interaction with other matter. Astronomers have identified numerous stellar black hole candidates in binary systems, by studying their interaction with their companion stars. There is growing consensus that supermassive black holes exist in the centers of most galaxies. In particular, there is apparently evidence of a black hole of more than 4 million solar masses at the center of our Milky Way, Sagittarius A*
One of the things that has been puzzling astrophysicists concerning our own (theorized) black hole, Sagittarius A* – the massive black hole at the center of the Milky Way – is its seeming lack of activity, when compared to similar objects in other galaxies. Now, experts are analyzing what would happen if the black hole were to wake up.
Over time, scientists measured Sagittarius A*’s mass at around 4 million solar masses, which makes it relatively small by comparison. For a galaxy the size of the Milky Way – 120,000 light-years across – one would expect to detect a supermassive black hole at least billions of solar masses in weight.
At the same time, high-energy measurements of the radio source have established that its level of radiation activity is several billion times weaker than it should be. Experts have always associated this with some kind of slumber. However, there are evidences that object occasionally returns to life.
Evidences collected from the very structure of the Milky Way appears to indicate that Sagittarius A* had an intense outburst about three hundred years ago, producing an extremely powerful flare.
However, confirming these theories is not as easy as proposing them. The galactic core is obscured by large clouds of hydrogen and dust and debris, making astronomical observations extremely difficult.
Distance is apparently another factor – though this brings us straight back to the original question, how is it that we are able to so easily discover dark energy in distant galaxies so easily?
“We have wondered why the Milky Way’s black hole appears to be a slumbering giant. But now we realize that the black hole was far more active in the past. Perhaps it’s just resting after a major outburst,” Kyoto University investigator Tatsuya Inui explains.
He and his team used the European Space Agency’s (ESA) XMM-Newton X-ray Observatory, the NASA Chandra X-ray Observatory, and the Japan Aerospace Exploration Agency’s (ESA) Suzaku and ASCA X-ray satellites to conduct this investigation.
Black holes of stellar mass are expected to form when massive stars collapse in a supernova at the end of their life cycle. After a black hole has formed it can continue to grow by absorbing mass from its surroundings. By absorbing other stars and merging with other black holes, supermassive black holes of millions of solar masses may be formed.
Related: The American Physical Society has just published http://physics.aps.org, In which researchers outline their hypothesis for smaller primordial Black Holes within our own galaxy.
Our galaxy could be filled with asteroid-size black holes that presumably formed shortly after the big bang. If they exist in large numbers, these so-called primordial black holes would serve as the dark matter that keeps stars gravitationally glued inside galaxies. None of these primordial black holes have been detected so far, but a new theoretical analysis described in Physical Review Letters demonstrates that a current planet-hunting mission is well placed to search for them.
As dark matter candidates go, primordial black holes are widely considered to be the dark horse. Previous astronomical searches for these objects came up empty, so many cosmologists put their money on the alternative candidate: a weakly interacting particle that physicists hope to find in accelerators or other experiments.
Still, there is a mass range of relatively small primordial black holes that has yet to be ruled out. Kim Griest, of the University of California in San Diego, and colleagues believe that part of this “observational gap” could be explored by piggybacking on a separate astronomy survey. NASA’s Kepler satellite was designed to search for planets around 150,000 stars (in a single field of view) that are relatively close to Earth. A planet passing in front of one of these stars dims the starlight by a small amount. Conversely, a black hole passing between us and a Kepler star would have the opposite effect: it would act as a lens and brighten the starlight. The authors calculate that Kepler is the first instrument sensitive enough to detect this so-called microlensing for black holes with masses of around 0.1% of an Earth mass. – Michael Schirber
In 1915, Albert Einstein developed his theory of general relativity, having earlier shown that gravity does influence light’s motion. Only a few months later, Karl Schwarzschild found a solution to Einstein field equations, which describes the gravitational field of a point mass and a spherical mass.
A few months after Schwarzschild, Johannes Droste, a student of Hendrik Lorentz, independently gave the same solution for the point mass and wrote more extensively about its properties.
This solution had a peculiar behaviour at what is now called the Schwarzschild radius, where it became singular, meaning that some of the terms in the Einstein equations became infinite. The nature of this surface was not quite understood at the time. In 1924, Arthur Eddington showed that the singularity disappeared after a change of coordinates, although it took until 1933 for Georges Lemaître to realize that this meant the singularity at the Schwarzschild radius was an unphysical coordinate singularity.
In 1931, Subrahmanyan Chandrasekhar calculated, using special relativity, that a non-rotating body of electron-degenerate matter above a certain limiting mass (now called the Chandrasekhar limit at 1.4 solar masses) has no stable solutions. His arguments were opposed by many of his contemporaries like Eddington and Lev Landau, who argued that some yet unknown mechanism would stop the collapse.
They were partly correct: a white dwarf slightly more massive than the Chandrasekhar limit will collapse into a neutron star, which is itself stable because of the Pauli exclusion principle. But in 1939, Robert Oppenheimer and others predicted that neutron stars above approximately three solar masses (the Tolman–Oppenheimer–Volkoff limit) would collapse into black holes for the reasons presented by Chandrasekhar, and concluded that no law of physics was likely to intervene and stop at least some stars from collapsing to black holes.
Oppenheimer and his co-authors interpreted the singularity at the boundary of the Schwarzschild radius as indicating that this was the boundary of a bubble in which time stopped. This is a valid point of view for external observers, but not for infalling observers. Because of this property, the collapsed stars were called “frozen stars,” because an outside observer would see the surface of the star frozen in time at the instant where its collapse takes it inside the Schwarzschild radius.
In 1958, David Finkelstein identified the Schwarzschild surface as an event horizon, “a perfect unidirectional membrane: causal influences can cross it in only one direction”. This did not strictly contradict Oppenheimer’s results, but extended them to include the point of view of infalling observers. Finkelstein’s solution extended the Schwarzschild solution for the future of observers falling into a black hole. 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 in 1967, which were shown to be rapidly rotating neutron stars by 1969. Until that time, neutron stars, like black holes, were regarded as just theoretical curiosities; but the discovery of pulsars showed their physical relevance and spurred a further interest in all types of compact objects that might be formed by gravitational collapse.
In this period more general black hole solutions were found. In 1963, 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. Through the work of Werner Israel, Brandon Carter, and David Robinson the no-hair theorem emerged, stating that a stationary black hole solution is completely described by the three parameters of the Kerr–Newman metric; mass, angular momentum, and electric charge.
For a long time, 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 sixties Roger Penrose and Stephen Hawking used global techniques to prove that singularities are generic.
Work by James Bardeen, Jacob Bekenstein, Carter, and Hawking in the early 1970s led to the formulation of black hole thermodynamics. These laws describe the behaviour of a black hole in close analogy to the laws of thermodynamics by relating mass to energy, area to entropy, and surface gravity to temperature. The analogy was completed when Hawking, in 1974, 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.
The term “black hole” was first publicly used by John Wheeler during a lecture in 1967. Although he is usually credited with coining the phrase, he always insisted that it was suggested to him by somebody else. The first recorded use of the term is in a 1964 letter by Anne Ewing to the American Association for the Advancement of Science. After Wheeler’s use of the term, it was quickly adopted in general use.
The no-hair theorem states that, once it achieves a stable condition after formation, a black hole has only three independent physical properties: mass, charge, and angular momentum. Any two black holes that share the same values for these properties, or parameters, are indistinguishable according to classical (i.e. non-quantum) mechanics.
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. Likewise, the angular momentum can be measured from far away using frame dragging by the gravitomagnetic field.
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.
This is different from other field theories like electromagnetism, which do not have any friction or resistivity at the microscopic level, because they are time-reversible. 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 the total baryon number, lepton number, and all the other nearly conserved pseudo-charges of particle physics. This behavior is so puzzling that it has been called the black hole information loss paradox.
The simplest black holes have mass but neither electric charge nor angular momentum. These black holes are often referred to as Schwarzschild black holes after Karl Schwarzschild who discovered this solution in 1916.
According to Birkhoff’s theorem, it is the only vacuum solution that is spherically symmetric. This means that there is no observable difference between the gravitational field of such a black hole and that of any other spherical object of the same mass. 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. Charged black holes are described by the Reissner–Nordström metric, while the Kerr metric describes a rotating black hole. 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. In Planck units, the total electric charge Q and the total angular momentum J are expected to satisfy for a black hole of mass M.
Black holes saturating 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. This is supported by numerical simulations.
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 common feature of compact objects. The black-hole candidate binary X-ray source GRS 1915+105 appears to have an angular momentum near the maximum allowed value.
Black holes are commonly classified according to their mass, independent of angular momentum J or electric charge Q. The size of a black hole, as determined by the radius of the event horizon, or Schwarzschild radius, is roughly proportional to the mass M through where rsh is the Schwarzschild radius and MSun is the mass of the Sun. This relation is exact only for black holes with zero charge and angular momentum; for more general black holes it can differ up to a factor of 2.
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. At the event horizon of a black hole, this deformation becomes so strong that there are no paths that lead away from the black hole.
To a distant observer, clocks near a black hole appear to tick more slowly than those further away from the black hole. Due to this effect, known as gravitational time dilation, an object falling into a black hole appears to slow down as it approaches the event horizon, taking an infinite time to reach it.
At the same time, all processes on this object slow down causing emitted light to appear redder and dimmer, an effect known as gravitational redshift. Eventually, at a point just before it reaches the event horizon, the falling object becomes so dim that it can no longer be seen.
On the other hand, an observer falling into a black hole does not notice any of these effects as he crosses the event horizon. According to his own clock, he crosses the event horizon after a finite time, although he is unable to determine exactly when he crosses it, as it is impossible to determine the location of the event horizon from local observations.
The shape of the event horizon of a black hole is always approximately spherical. For non-rotating (static) black holes the geometry is precisely spherical, while for rotating black holes the sphere is somewhat oblated.
At the center of a black hole as described by general relativity lies a gravitational singularity, a region where the spacetime curvature becomes infinite. For a non-rotating black hole this region takes the shape of a single point and for a rotating black hole it is smeared out to form a ring singularity lying in the plane of rotation. In both cases the singular region has zero volume. It can also be shown that the singular region contains all the mass of the black hole solution. The singular region can thus be thought of as having infinite density.
Observers falling into a Schwarzschild black hole (i.e. non-rotating and no charges) cannot avoid being carried into the singularity, once they cross the event horizon. They can prolong the experience by accelerating away to slow their descent, but only up to a point; after attaining a certain ideal velocity, it is best to free fall the rest of the way. When they reach the singularity, they are crushed to infinite density and their mass is added to the total of the black hole. 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.
In the case of a charged (Reissner–Nordström) or rotating (Kerr) black hole it is possible to avoid the singularity. 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 possibility of traveling to another universe is however only theoretical, since any perturbation will destroy this possibility. It also appears to be possible to follow closed timelike curves (going back to one’s own past) around the Kerr singularity, which lead to problems with causality like the grandfather paradox. It is expected that none of these peculiar effects would survive in a proper quantum mechanical treatment of rotating and charged black holes.
The appearance of singularities in general relativity is commonly perceived as signaling the breakdown of the theory. This breakdown, however, is expected; it occurs in a situation where quantum mechanical effects should describe these actions due to the extremely high density and therefore particle interactions. To date it has not been possible to combine quantum and gravitational effects into a single theory. It is generally expected that a theory of quantum gravity will feature black holes without singularities.
The photon sphere is a spherical boundary of zero thickness such that photons moving along tangents to the sphere will be trapped in a circular orbit. For non-rotating black holes, the photon sphere has a radius 1.5 times the Schwarzschild radius. The orbits are dynamically unstable, hence any small perturbation (such as a particle of infalling matter) will grow over time, either setting it on an outward trajectory escaping the black hole or on an inward spiral eventually crossing the event horizon.
While light can still escape from inside the photon sphere, any light that crosses the photon sphere on an inbound trajectory will be captured by the black hole. Hence any light reaching an outside observer from inside the photon sphere must have been emitted by objects inside the photon sphere but still outside of the event horizon.
Other compact objects, such as neutron stars, can also have photon spheres. This follows from the fact that the gravitational field of an object does not depend on its actual size, hence any object that is smaller than 1.5 times the Schwarzschild radius corresponding to its mass will indeed have a photon sphere.
Considering the exotic nature of black holes, it may be natural to question if such bizarre objects could exist in nature or to suggest that they are 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. This led the general relativity community to dismiss all results to the contrary for many years. However, a minority of relativists continued to contend that black holes were physical objects, and by the end of the 1960s, they had persuaded the majority of researchers in the field that there is no obstacle to forming an event horizon.
Once an event horizon forms, Penrose proved that a singularity will form somewhere inside it. Shortly afterwards, Hawking showed that many cosmological solutions describing the Big Bang have singularities without scalar fields or other exotic matter (see Penrose-Hawking singularity theorems). The Kerr solution, the no-hair theorem and the laws of black hole thermodynamics showed that the physical properties of black holes were simple and comprehensible, making them respectable subjects for research. The primary formation process for black holes is expected to be the gravitational collapse of heavy objects such as stars, but there are also more exotic processes that can lead to the production of black holes.
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 ideal gas law explains the connection between pressure, temperature, and volume.
The collapse may be stopped by the degeneracy pressure of the star’s constituents, condensing the matter in an exotic denser state. The result is one of the various types of compact star. The type of compact star formed depends on the mass of the remnant—the matter left over after the outer layers have been blown away, such from a supernova explosion or by pulsations leading to a planetary nebula. Note that this mass can be substantially less than the original star—remnants exceeding 5 solar masses are produced by stars that were over 20 solar masses before the collapse.
If the mass of the remnant exceeds about 3–4 solar masses (the Tolman–Oppenheimer–Volkoff limit)—either because the original star was very heavy or because the remnant collected additional mass through accretion of matter—even the degeneracy pressure of neutrons is insufficient to stop the collapse. 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. Star formation in the early universe may have resulted in very massive stars, which upon their collapse would have produced black holes of up to 103 solar masses. 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 sees 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 is 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.
Primordial Black Holes
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. The high density alone is not enough to allow the formation of black holes since a uniform mass distribution will not allow the mass to bunch up.
In order for primordial black holes to form in such a dense medium, there must be initial density perturbations that can then grow under their own gravity. Different models for the early universe vary widely in their predictions of the size of these perturbations. Various models predict the creation of black holes, ranging from a Planck mass to hundreds of thousands of solar masses. Primordial black holes could thus account for the creation of any type of black hole.
High Energy Collisions
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 2002, no such events have been detected, either directly or indirectly as a deficiency of the mass balance in particle accelerator experiments.
This suggests that there must be a lower limit for the mass of black holes. Theoretically, this boundary is expected to lie around the Planck mass (mP = √ħc/G ≈ 1.2×1019 GeV/c2 ≈ 2.2×10−8 kg), where quantum effects are expected to invalidate the predictions of general relativity. This would put the creation of black holes firmly out of reach of any high energy process occurring on or near the Earth. However, certain developments in quantum gravity suggest that the Planck mass could be much lower: some braneworld scenarios for example put the boundary as low as 1 TeV/c2.
This would make it conceivable for micro black holes to be created in the high energy collisions occurring when cosmic rays hit the Earth’s atmosphere, or possibly in the new Large Hadron Collider at CERN. Yet these theories are very speculative, and the creation of black holes in these processes is deemed unlikely by many specialists. Even if micro black holes should be formed in these collisions, it is expected that they would evaporate in about 10−25 seconds, posing no threat to the Earth.
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 direct surroundings and omnipresent cosmic background radiation. This is the primary process through which supermassive black holes seem to have grown. A similar process has been suggested for the formation of intermediate-mass black holes in globular clusters.
Another possibility is for a black hole to merge with other objects such as stars or even other black holes. This is thought to have been important especially for the early development of supermassive black holes, which could have formed from the coagulation of many smaller objects. The process has also been proposed as the origin of some intermediate-mass black holes.
In 1974, Stephen Hawking showed that black holes are not entirely black but emit small amounts of thermal radiation. He got this result by applying quantum field theory in a static black hole background. The result of his calculations is that a black hole should emit particles in a perfect black body spectrum.
This effect has become known as Hawking radiation. Since Hawking’s result, many others have verified the effect through various methods. If his theory of black hole radiation is correct, then black holes are expected to emit a thermal spectrum of radiation, and thereby lose mass (the mass possessed by the photons and other particles emitted). Black holes will shrink and evaporate over time. The temperature of this spectrum (Hawking temperature) is proportional to the surface gravity of the black hole, which for a Schwarzschild black hole is inversely proportional to the mass. Large black holes, therefore, emit less radiation than small black holes.
A stellar black hole of one solar mass has a Hawking temperature of about 100 nanokelvins. This is far less than the 2.7 K temperature of the cosmic microwave background. Stellar mass (and larger) black holes receive more mass from the cosmic microwave background than they emit through Hawking radiation and will thus grow instead of shrink. To have a Hawking temperature larger than 2.7 K (and be able to evaporate), a black hole needs to be lighter than the Moon (and therefore a diameter of less than a tenth of a millimeter).
On the other hand, if a black hole is very small the radiation effects are expected to become very strong. Even a black hole that is heavy compared to a human would evaporate in an instant. A black hole the weight of a car (~10−24 m) would only take a nanosecond to evaporate, during which time it would briefly have a luminosity more than 200 times that of the sun. Lighter black holes are expected to evaporate even faster; for example, a black hole of mass 1 TeV/c2 would take less than 10−88 seconds to evaporate completely. Of course, for such a small black hole quantum gravitation effects are expected to play an important role and could even—although current developments in quantum gravity do not indicate so—hypothetically make such a small black hole stable.
By their very nature, black holes do not directly emit any signals other than the hypothetical Hawking radiation; since the Hawking radiation for an astrophysical black hole is predicted to be very weak, this makes it impossible to directly detect astrophysical black holes from the Earth. A possible exception to the Hawking radiation being weak is the last stage of the evaporation of light (primordial) black holes; searches for such flashes in the past has proven unsuccessful and provides stringent limits on the possibility of existence of light primordial black holes.
NASA’s Fermi Gamma-ray Space Telescope launched in 2008 will continue the search for these flashes. Astrophysicists searching for black holes thus have to rely on indirect observations. A black hole’s existence can sometimes be inferred by observing its gravitational interactions with its surroundings.
The deformation of spacetime around a massive object causes light rays to be deflected much like light passing through an optic lens. This phenomenon is known as gravitational lensing. Observations have been made of weak gravitational lensing, in which photons are deflected by only a few arcseconds. However, it has never been directly observed for a black hole.
One possibility for observing gravitational lensing by a black hole would be to observe stars in orbit around the black hole. There are several candidates for such an observation in orbit around Sagittarius A*
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.
A phase of free quarks at high density might allow the existence of dense quark stars, and some supersymmetric models predict the existence of Q stars. Some extensions of the standard model posit the existence of preons as fundamental building blocks of quarks and leptons, which could hypothetically form preon stars.
These hypothetical models could potentially explain a number of observations of stellar black hole candidates. However, it can be shown from general arguments in general relativity that any such object will have a maximum mass.
Since the average density of a black hole inside its Schwarzschild radius is inversely proportional to the square of its mass, supermassive black holes are much less dense than stellar black holes (the average density of a 108 solar mass black hole is comparable to that of water).
Consequently, the physics of matter forming a supermassive black hole is much better understood and the possible alternative explanations for supermassive black hole observations are much more mundane. For example, a supermassive black hole could be modelled by a large cluster of very dark objects. However, typically such alternatives are not stable enough to explain the supermassive black hole candidates
The evidence for stellar and supermassive black holes implies that in order for black holes not to 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 no black holes).
In recent years, much attention has been drawn by the fuzzball model in string theory. Based on calculations in specific situations in string theory, the proposal suggest that generically the individual states of a black hole solution do not have an event horizon or singularity, but that for a classical/semi-classical observer the statistical average of such states does appear just like an ordinary black hole in general relativity
In 1971, Hawking showed under general conditions that the total area of the event horizons of any collection of classical black holes can never decrease, even if they collide and merge. This result, now known as the second law of black hole mechanics, is remarkably similar to the second law of thermodynamics, which states that the total entropy of a system can never decrease. 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. 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. In 1995, Andrew Strominger and Cumrun Vafa showed that counting the microstates of a specific supersymmetric black hole in string theory reproduced the Bekenstein–Hawking entropy.
Since then, similar results have been reported for different black holes both in string theory and in other approaches to quantum gravity like loop quantum gravity.
An open question in fundamental physics is the so-called information loss paradox, or black hole unitarity paradox. Classically, the laws of physics are the same run forward or in reverse (T-symmetry). Liouville’s theorem dictates conservation of phase space volume, which can be thought of as “conservation of information”, so there is some problem even in classical physics. In quantum mechanics, this corresponds to a vital property called unitarity, which has to do with the conservation of probability (it can also be thought of as a conservation of quantum phase space volume as expressed by the density matrix)
- Popular reading
- Ferguson, Kitty (1991). Black Holes in Space-Time. Watts Franklin. ISBN 0-531-12524-6.
- Hawking, Stephen (1988). A Brief History of Time. Bantam Books, Inc. ISBN 0-553-38016-8.
- Hawking, Stephen; Penrose, Roger (1996). The Nature of Space and Time. Princeton University Press. ISBN 0-691-03791-2.
- Melia, Fulvio (2003). The Black Hole at the Center of Our Galaxy. Princeton U Press. ISBN 978-0-691-09505-9.
- Melia, Fulvio (2003). The Edge of Infinity. Supermassive Black Holes in the Universe. Cambridge U Press. ISBN 978-0-521-81405-8.
- Pickover, Clifford (1998). Black Holes: A Traveler’s Guide. Wiley, John & Sons, Inc. ISBN 0-471-19704-1.
- Stern, B. (2008). “Blackhole”., poem.
- Thorne, Kip S. (1994). Black Holes and Time Warps. Norton, W. W. & Company, Inc. ISBN 0-393-31276-3.
- Wheeler, J. Craig (2007). Cosmic Catastrophes (2nd ed.). Cambridge University Press. ISBN 0-521-85714-7.
- University textbooks and monographs
- Carroll, Sean M. (2004). Spacetime and Geometry. Addison Wesley. ISBN 0-8053-8732-3., the lecture notes on which the book was based are available for free from Sean Carroll’s website.
- Carter, B. (1973). “Black hole equilibrium states”. In DeWitt, B.S.; DeWitt, C.. Black Holes.
- Chandrasekhar, Subrahmanyan (1999). Mathematical Theory of Black Holes. Oxford University Press. ISBN 0-19-850370-9.
- Frolov, V.P.; Novikov, I.D. (1998). Black hole physics.
- Hawking, S.W.; Ellis, G.F.R. (1973). Large Scale Structure of space time. Cambridge University Press. ISBN 0521099064.
- Melia, Fulvio (2007). The Galactic Supermassive Black Hole. Princeton U Press. ISBN 978-0-691-13129-0.
- Taylor, Edwin F.; Wheeler, John Archibald (2000). Exploring Black Holes. Addison Wesley Longman. ISBN 0-201-38423-X.
- Thorne, Kip S.; Misner, Charles; Wheeler, John (1973). Gravitation. W. H. Freeman and Company. ISBN 0-7167-0344-0.
- Wald, Robert M. (1984). General Relativity. University of Chicago Press. ISBN 978-0-226-87033-5.
- Wald, Robert M. (1992). Space, Time, and Gravity: The Theory of the Big Bang and Black Holes. University of Chicago Press. ISBN 0-226-87029-4.
- Review papers
- Gallo, Elena; Marolf, Donald (2009). “Resource Letter BH-2: Black Holes”. American Journal of Physics 77 (4): 294. arXiv:0806.2316. Bibcode2009AmJPh..77..294G. doi:10.1119/1.3056569.
- Hughes, Scott A. (2005). “Trust but verify: The case for astrophysical black holes”. arXiv:hep-ph/0511217 [hep-ph]. Lecture notes from 2005 SLAC Summer Institute.
- Black Holes on In Our Time at the BBC
- Stanford Encyclopedia of Philosophy: Singularities and Black Holes
- Black Hole
- Black Holes: Gravity’s Relentless Pull
- FAQ on black holes
- Schwarzschild Geometry
- Advanced Mathematics of Black Hole Evaporation