Black Holes

A black hole is a region of spacetime from which gravity prevents anything, including light, from escaping. 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. The hole is called "black" because it absorbs all the light that hits the horizon, reflecting nothing, just like a perfect black body in thermodynamics.

Quantum field theory in curved spacetime predicts that event horizons 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.

Objects whose gravity fields are 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 first published by David Finkelstein in 1958. 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.

Black holes of stellar mass are expected to form when very massive stars collapse 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 form. There is general consensus that supermassive black holes exist in the centers of most galaxies.

Despite its invisible interior, the presence of a black hole can be inferred through its interaction with other matter and with electromagnetic radiation such as light. Matter falling onto a black hole can form an accretion disk heated by friction, forming some of the brightest objects in the universe. If there are other stars orbiting a black hole, their orbit can be used to determine its mass and location. These data can be used to exclude possible alternatives (such as neutron stars). In this way, astronomers have identified numerous stellar black hole candidates in binary systems, and established that the core of our Milky Way galaxy contains a supermassive black hole of about 4.3 million solar masses.

The concept of a body so massive that not even light could escape from it was put forward by the English geologist John Michell in a 1783 paper sent to the Royal Society. At that time, the Newtonian theory of gravity and the concept of escape velocity were well known. Michell computed that a body 500 times the radius of the Sun and of the same density would have at its surface an escape velocity equal to the speed of light, and therefore would be invisible. Although he thought it unlikely, Michell considered the possibility that many such objects that cannot be seen might be present in the cosmos.

In 1796, the French mathematician Pierre-Simon Laplace promoted the same idea in the first and second edition of his book Exposition du Systeme du Monde. It disappeared in later editions. The whole idea gained little attention in the 19th century, since light was thought to be a massless wave, not influenced by gravity.

Spacetime Curvature

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 the Einstein field equations, which describes the gravitational field of a point mass and a spherical mass.[8] 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 behavior 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 (see EddingtonÐFinkelstein coordinates), although it took until 1933 for Georges Lema”tre 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 TolmanÐOppenheimerÐVolkoff 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. p the collapse. His arguments were opposed by Arthur Eddington, who believed that something would inevitably stop the collapse.

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.

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 KerrÐNewman metric; mass, angular momentum, and electric charge.

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, by 1969, were shown to be rapidly rotating neutron stars. 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.

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 1960s Roger Penrose and Stephen Hawking used global techniques to prove that singularities appear generically.

The first use of the term "black hole" in print was by journalist Ann Ewing in her article "'Black Holes' in Space", dated 18 January 1964, which was a report on a meeting of the American Association for the Advancement of Science.

John Wheeler used term "black hole" a lecture in 1967, leading some to credit him with coining the phrase. After Wheeler's use of the term, it was quickly adopted in general use.

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 behavior 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.

No Black Holes Exist, Says Stephen Hawking - At Least Not Like We Think National Geographic - January 27, 2014

Black holes do not exist - at least, not as we know them, says renowned physicist Stephen Hawking, potentially provoking a rethink of one of space's most mysterious objects. A new study from Hawking also says that black holes may not possess "firewalls," destructive belts of radiation that some researchers have proposed would incinerate anything that passes through them but others scientists deem an impossibility. The conventional view of black holes posits that their gravitational pull is so powerful that nothing can escape from them - not even light, which is why they're called black holes. The boundary past which there is supposedly no return is known as the event horizon. In this conception, all information about anything that ventures past a black hole's event horizon is destroyed. On the other hand, quantum physics, the best description so far of how the universe behaves on a subatomic level, suggests that information cannot ever be destroyed, leading to a fundamental conflict in theory. Now Hawking is suggesting a resolution to the paradox: Black holes do not possess event horizons after all, so they do not destroy information.

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, for a fixed outside observer, causing emitted light to appear redder and dimmer, an effect known as gravitational redshift.[49] 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 without noting any singular behavior. In particular, 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 oblate.

Black hole hums B flat BBC - September 10, 2003

Astronomers have detected sound waves from a super-massive black hole. The "note" is the deepest ever detected from an object in the Universe. The black hole lives in the Perseus cluster of galaxies, located 250 million light-years away. The tremendous amounts of energy carried from the black hole by these sound waves may solve a longstanding problem in astrophysics. The pitch of the sound can be determined. Although far too low to be heard, it is calculated to be B flat.

At the center of the black hole, well inside the event horizon, general relativity predicts a singularity, a place where the curvature of space-time becomes infinite and gravitational forces become infinitely strong. Space-time inside the event horizon is peculiar in that the singularity is in every observer's future, so all particles within the event horizon move inexorably towards it. This means that there is a conceptual inaccuracy in the non-relativistic concept of a black hole as originally proposed by John Michell in 1783.

It is expected that future refinements or generalizations of general relativity (in particular quantum gravity) will change what is thought about the nature of black hole interiors. Most theorists interpret the mathematical singularity of the equations as indicating that the current theory is not complete, and that new phenomena must come into play as one approaches the singularity. The question may be largely academic, as the cosmic censorship hypothesis asserts that there are no naked singularities in general relativity: Every singularity is hidden behind an event horizon and cannot be probed.

Another school of thought holds that no singularity occurs, because of a bubble-like local inflation in the interior of the collapsing star. Radii stop converging as they approach the event horizon, are parallel at the horizon, and begin diverging in the interior. The solution resembles a wormhole (from the exterior to the interior) in a neighborhood of the horizon, with the horizon as the neck.

In Michell's theory, the escape velocity equals the speed of light, but it would still, for example, be theoretically possible to hoist an object out of a black hole using a rope. General relativity eliminates such loopholes, because once an object is inside the event horizon, its time-line contains an end-point to time itself, and no possible world-lines come back out through the event horizon.

According to theory, the event horizon of a black hole that is not spinning is spherical, and its singularity is (informally speaking) a single point. If the black hole carries angular momentum (inherited from a star that is spinning at the time of its collapse), it begins to drag space-time surrounding the event horizon in an effect known as frame-dragging.

This spinning area surrounding the event horizon is called the ergosphere and has an ellipsoidal shape. Since the ergosphere is located outside the event horizon, objects can exist within the ergosphere without falling into the hole. However, because space-time itself is moving in the ergosphere, it is impossible for objects to remain in a fixed position. Objects grazing the ergosphere could in some circumstances be catapulted outwards at great speed, extracting energy (and angular momentum) from the hole, hence the name ergosphere ("sphere of work") because it is capable of doing work.

The effects of a black hole's gravity as described by the Theory of Relativity cause a number of peculiar effects. An object approaching simple Schwarzschild-type (non-rotating) black hole's center will appear to distant observers as having an increasingly slow descent as the object approaches the event horizon. This is because a photon takes an increasingly long time to escape from the pull of the black hole to allow the distant observer to gain information on the object's fate.

From the object's frame of reference, it will cross the event horizon and reach the singularity, or center of the black hole, all within a finite amount of time. Once the object crosses over the event horizon, light will no longer escape the black hole, and the object can no longer be observed outside of the black hole. As the object continues to approach the singularity, it will elongate, and the parts closest to the singularity will begin to red shift, until they finally become invisible. Nearing the singularity, the gradient of the gravitational field from head to foot will become considerable, will stretch and tear because of tidal forces: the parts closest to the singularity feel disproportionately stronger gravitational force than those parts farther away. This process is known as spaghetti-fication.

In 1971, Stephen Hawking showed that the total area of the event horizons of any collection of classical black holes can never decrease. This sounded remarkably similar to the Second Law of Thermodynamics, with area playing the role of entropy. Classically, one could violate the second law of thermodynamics by material entering a black hole disappearing from our universe and resulting in a decrease of the total entropy of the universe.

Therefore, Jacob Bekenstein proposed that a black hole should have an entropy and that it should be proportional to its horizon area. Since black holes do not classically emit radiation, the thermodynamic viewpoint was simply an analogy. However, in 1974, Hawking applied quantum field theory to the curved space-time around the event horizon and discovered that black holes can emit thermal radiation, known as Hawking radiation.

Using the first law of black hole mechanics, it follows that the entropy of a black hole is one quarter of the area of the horizon. This is a universal result and can be extended to apply to cosmological horizons such as in de Sitter spacetime. It was later suggested that black holes are maximum-entropy objects, meaning that the maximum entropy of a region of space is the entropy of the largest black hole that can fit into it. This led to the holographic principle.

Hawking radiation originates just outside the event horizon and, so far as it is understood, does not carry information from its interior since it is thermal. However, this means that black holes are not completely black: the effect implies that the mass of a black hole slowly evaporates with time. Although these effects are negligible for astronomical black holes, they are significant for hypothetical very small black holes where quantum-mechanical effects dominate. Indeed, small black holes are predicted to undergo runaway evaporation and eventually vanish in a burst of radiation. Hence, every black hole that cannot consume new mass has a finite life that is directly related to its mass.

On 21 July 2004 Stephen Hawking presented a new argument that black holes do eventually emit information about what they swallow, reversing his previous position on information loss. He proposed that quantum perturbations of the event horizon could allow information to escape from a black hole, where it can influence subsequent Hawking radiation . The theory has not yet been reviewed by the scientific community and if it is accepted it is likely to resolve the black hole information paradox. In the meantime, the announcement has attracted a lot of attention in the media.

General relativity (as well as most other metric theories of gravity) not only says that black holes can exist, but in fact predicts that they will be formed in nature whenever a sufficient amount of mass gets packed in a given region of space, through a process called gravitational collapse. As the mass inside that region increases, its gravity becomes stronger - or, in the language of relativity, the space around it becomes increasingly deformed. When the escape velocity at a certain distance from the center reaches the speed of light, an event horizon is formed within which matter must inevitably collapse onto a single point, forming a singularity.

A quantitative analysis of this idea led to the prediction that a star remaining about three times the mass of the Sun at the end of its evolution (usually as a neutron star), will almost inevitably shrink to the critical size needed to undergo a gravitational collapse. Once it starts, the collapse cannot be stopped by any physical force, and a black hole is created.

Stellar collapse will generate black holes containing at least three solar masses. Black holes smaller than this limit can only be created if their matter is subjected to sufficient pressure from some source other than self-gravitation. The enormous pressures needed for this are thought to have existed in the very early stages of the universe, possibly creating primordial black holes which could have masses smaller than that of the Sun.

Supermassive black holes containing millions to billions of solar masses could also form wherever a large number of stars are packed in a relatively small region of space, or by large amounts of mass falling into a "seed" black hole, or by repeated fusion of smaller black holes. The necessary conditions are believed to exist in the centers of some (if not most) galaxies, including our own Milky Way .

Theory says that we cannot detect black holes by light that is emitted or reflected by the matter inside them. However, those objects can be inductively detected from observation of phenomena near them, such as gravitational lensing and stars that appear to be in orbit around space where there is no visible matter.

The most conspicuous effects are believed to come from matter falling into a black hole, which (like water flowing into a drain) is predicted to collect into an extremely hot and fast-spinning accretion disk around the object before being swallowed by it. Friction between adjacent zones of the disk causes it to become extremely hot and emit large amounts of X-rays. This heating is extremely efficient and can convert about 50% of the mass energy of an object into radiation, as opposed to nuclear fusion which can only convert a few percent of the mass to energy. Other predicted effects are narrow jets of particles at relativistic speeds squirting off along the disk's axis.

However, accretion disks, jets, and orbiting objects are found not only around black holes, but also around other objects such as neutron stars; and the dynamics of bodies near these non-black hole attractors is largely similar to the dynamics of bodies around black holes, and is currently a very complex and active field of research involving magnetic fields and plasma physics.

Hence, for the most part, observations of accretion disks and orbital motions merely indicate that there is a compact object of a certain mass, and says very little about 'the nature of that object. The identification of an object as a black hole requires the further assumption that no other object (or bound system of objects) could be so massive and compact. Most astrophysicists accept that this is the case, since according to general relativity, any concentration of matter of sufficient density must necessarily collapse into a black hole.

One important observable difference between black holes and other compact massive objects is that any in falling matter will eventually collide with the latter, at relativistic speeds, leading to irregular intense flares of X-rays and other hard radiation. Thus the lack of such flare-ups around a compact concentration of mass is taken as evidence that the object is a black hole, with no surface onto which matter can be suddenly dumped.

The formation of micro black holes on Earth in particle accelerators have been tentatively reported, but not yet confirmed. So far there are no observed candidates for primordial black holes. Read more ...