The idea of a body so massive that even light could not escape was put forward by geologist John Michell in a letter written to Henry Cavendish in 1783 to 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.—John Michell[2]
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).[3][4] Such "dark stars" were largely ignored in the nineteenth century, since light was then thought to be a massless wave and therefore not influenced by gravity. Unlike the modern black hole concept, the object behind the horizon of a dark star is assumed to be stable against collapse.
General Relativity
In 1915, Albert Einstein developed his general theory of relativity, having earlier shown that gravity does in fact influence light's motion. A few months later, Karl Schwarzschild gave the solution for the gravitational field of a point mass and a spherical mass,[5] showing that a black hole could theoretically exist. The Schwarzschild radius is now known to be the radius of the event horizon of a non-rotating black hole, but this was not well understood at that time, for example Schwarzschild himself thought it was not physical. Johannes Droste, a student of Hendrik Lorentz, independently gave the same solution for the point mass a few months after Schwarzschild and wrote more extensively about its properties. In 1930, astrophysicist Subrahmanyan Chandrasekhar calculated, using general relativity, that a non-rotating body of electron-degenerate matter above 1.44 solar masses (the Chandrasekhar limit) would collapse. His arguments were opposed by Arthur Eddington, who believed that something would inevitably stop the collapse. Eddington was 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 stars above approximately three solar masses (the Tolman-Oppenheimer-Volkoff limit) would collapse into black holes for the reasons presented by Chandrasekhar.[6] Oppenheimer and his co-authors used Schwarzschild's system of coordinates (the only coordinates available in 1939), which produced mathematical singularities at the Schwarzschild radius, in other words some of the terms in the equations became infinite at the Schwarzschild radius. This was interpreted as indicating that the Schwarzschild radius 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,"[7] 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. This is a known property of modern black holes, but it must be emphasized that the light from the surface of the frozen star becomes redshifted very fast, turning the black hole black very quickly. Many physicists could not accept the idea of time standing still at the Schwarzschild radius, and there was little interest in the subject for over 20 years.
Golden age
In 1958, David Finkelstein introduced the concept of the event horizon by presenting Eddington-Finkelstein coordinates, which enabled him to show that "The Schwarzschild surface r = 2 m is not a singularity, but that it acts as a perfect unidirectional membrane: causal influences can cross it in only one direction".[8] This did not strictly contradict Oppenheimer's results, but extended them to include the point of view of infalling observers. All theories up to this point, including Finkelstein's, covered only non-rotating black holes. In 1963, Roy Kerr found the exact solution for a rotating black hole. The rotating singularity of this solution was a ring, and not a point. A short while later, Roger Penrose was able to prove that singularities occur inside any black hole. In 1967, astronomers discovered pulsars,[9][10] and within a few years could show that the known pulsars were rapidly rotating neutron stars. Until that time, neutron stars were also regarded as just theoretical curiosities. So the discovery of pulsars awakened interest in all types of ultra-dense objects that might be formed by gravitational collapse.
Physicist John Wheeler is widely credited with coining the term black hole in his 1967 public lecture Our Universe: the Known and Unknown, as an alternative to the more cumbersome "gravitationally completely collapsed star." However, Wheeler insisted that someone else at the conference had coined the term and he had merely adopted it as useful shorthand. The term was also cited in a 1964 letter by Anne Ewing to the AAAS:
According to Einstein’s general theory of relativity, as mass is added to a degenerate star a sudden collapse will take place and the intense gravitational field of the star will close in on itself. Such a star then forms a "black hole" in the universe.—Ann Ewing, letter to AAAS[11]
Properties and structure
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.[12] Any two black holes that share the same values for these properties, or parameters, are classically indistinguishable.
These properties are special because they are visible from outside the black hole. For example, a charged black hole repels other like charges just like any other charged object, despite the fact that photons, the particles responsible for electric and magnetic forces, cannot escape from the interior region. The reason is Gauss's law, the total electric flux going out of a big sphere always stays the same, and measures the total charge inside the sphere. When charge falls into a black hole, electric field lines still remain, poking out of the horizon, and these field lines conserve the total charge of all the infalling matter. The electric field lines eventually spread out evenly over the surface of the black hole, forming a uniform field-line density on the surface. The black hole acts in this regard like a classical conducting sphere with a definite resistivity.[13] Similarly, the total mass inside a sphere containing a black hole can be found by using the gravitational analog of Gauss's law, far away from the black hole. Likewise, the angular momentum can be measured from far away using frame dragging by the gravitomagnetic field.
When a black hole swallows any form of matter, its horizon oscillates like a stretchy membrane with friction, a dissipative system, until it reaches a simple final state. This is different from other field theories like electromagnetism or gauge theory, which never have any friction or resistivity, because they are time reversible. Because the 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 the 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.[14][15][16]
Classification
By physical properties
The simplest black hole has mass but neither charge nor angular momentum. These black holes are often referred to as Schwarzschild black holes after the physicist Karl Schwarzschild who discovered this solution in 1915.[5] It was the first non-trivial exact solution to the Einstein field equations to be discovered, and according to Birkhoff's theorem, the only vacuum solution that is spherically symmetric.[17] 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 the black hole horizon; far away, the external gravitational field is identical to that of any other body of the same mass.[18]
More general black hole solutions were discovered later in the 20th century. The Reissner-Nordström metric describes a black hole with electric charge, while the Kerr metric yields a rotating black hole. The more generally known stationary black hole solution, the Kerr-Newman metric, describes 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 natural units , the total charge 
for a black hole of mass M.
Black holes saturating this inequality are called extremal. Solutions of Einstein's equations violating the inequality do exist, but do not have a horizon. These solutions have naked singularities and are deemed unphysical, as the cosmic censorship hypothesis rules out such singularities due to the generic gravitational collapse of realistic matter.[19] This is supported by numerical simulations.[20]
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, and the black-hole candidate binary X-ray source GRS 1915+105[21] appears to have an angular momentum near the maximum allowed value.
By mass
| Class | Mass | Size |
|---|---|---|
| Supermassive black hole | ~105–109 MSun | ~0.001–10 AU |
| Intermediate-mass black hole | ~103 MSun | ~103 km = REarth |
| Stellar-mass | ~10 MSun | ~30 km |
| Micro black hole | up to ~MMoon | up to ~0.1 mm |
Black holes are commonly classified according to their mass, independent of angular momentum 
where 
- Supermassive – contain hundreds of thousands to billions of solar masses, and are thought to exist in the center of most galaxies,[22][23] including the Milky Way.[24] They are thought to be responsible for active galactic nuclei, and presumably form either from the coalescence of smaller black holes, or by the accretion of stars and gas onto them. The largest known supermassive black hole is located in OJ 287 weighing in at 18 billion solar masses.[25]
- Intermediate – contain thousands of solar masses. They have been proposed as a possible power source for ultraluminous X-ray sources.[26] There is no known mechanism for them to form directly, so they likely form via collisions of lower mass black holes, either in the dense stellar cores of globular clusters or galaxies.[citation needed] Such creation events should produce intense bursts of gravitational waves, which may be observed soon. The boundary between super- and intermediate-mass black holes is a matter of convention. Their lower mass limit, the maximum mass for direct formation of a single black hole from collapse of a massive star, is poorly known at present, but is thought to be somewhere well below 200 solar masses.
- Stellar-mass – have masses ranging from a lower limit of about 1.4–3 solar masses (1.4 is the Chandrasekhar limit and 3 is the Tolman-Oppenheimer-Volkoff limit for the maximum mass of neutron stars) up to perhaps 15–20 solar masses. They are created by the collapse of individual stars, or by the coalescence (inevitable, due to gravitational radiation) of binary neutron stars. Stars may form with initial masses up to about 100 solar masses, or in the distant past, possibly even higher, but these shed most of their outer massive layers during earlier phases of their evolution, either blown away in stellar winds during the red giant, AGB, and Wolf-Rayet stages, or expelled in supernova explosions for stars that turn into neutron stars or black holes. Being known mostly by theoretical models for late-stage stellar evolution, the upper limit for the mass of stellar-mass black holes is somewhat uncertain at present. The cores of still lighter stars form white dwarfs.
- Micro – (also mini black holes) have masses much less than that of a star. At these sizes, quantum mechanics is expected to take effect. There is no known mechanism for them to form via normal processes of stellar evolution, but certain inflationary scenarios predict their production during the early stages of the evolution of the universe.[citation needed] According to some theories of quantum gravity they may also be produced in the highly energetic reaction produced by cosmic rays hitting the atmosphere or even in particle accelerators such as the Large Hadron Collider.[citation needed] The theory of Hawking radiation predicts that such black holes will evaporate in bright flashes of gamma radiation. NASA's Fermi Gamma-ray Space Telescope satellite (formerly GLAST) launched in 2008 is searching for such flashes.[27]
Event horizon
 Far away from the black hole a particle can move in any direction. It is only restricted by the speed of light. |
 Closer to the black hole spacetime starts to deform. There are more paths going towards the black hole than paths moving away. |
 Inside of the event horizon all paths bring the particle closer to the center of the black hole. It is no longer possible for the particle to escape. |
The defining feature of a black hole is the appearance of an event horizon; a boundary in spacetime beyond which events cannot affect an outside observer. As predicted by general relativity, the presence of a mass deforms spacetime in such a way that the paths particles take tend towards the mass. At the event horizon of a black hole this deformation becomes so strong that there are no more paths that lead away from the black hole.[28] Once a particle is inside the horizon, moving into the hole is as inevitable as moving forward in time (and can actually be thought of as equivalent to doing so).
To a distant observer clocks near a black hole appear to tick more slowly than those further away from the black hole.[29] Due to this effect (known as gravitational time dilation) the distant observer will see an object falling into a black hole slow down as it approaches the event horizon, taking an infinite time to reach it.[30] At the same time all processes on this object slow down causing emitted light to appear redder and dimmer, an effect known as gravitational red shift.[31] Eventually, the falling object becomes so dim that it can no longer be seen, at a point just before it reaches the event horizon.
For a non rotating (static) black hole, the Schwarzschild radius delimits a spherical event horizon. The Schwarzschild radius of an object is proportional to the mass.[32] Rotating black holes have distorted, nonspherical event horizons. Since the event horizon is not a material surface but rather merely a mathematically defined demarcation boundary, nothing prevents matter or radiation from entering a black hole, only from exiting one. The description of black holes given by general relativity is known to be an approximation, and it is expected that quantum gravity effects become significant near the vicinity of the event horizon.[33] This allows observations of matter in the vicinity of a black hole's event horizon to be used to indirectly study general relativity and proposed extensions to it.
Though black holes themselves may not radiate energy, electromagnetic radiation and matter particles may be radiated from just outside the event horizon via Hawking radiation.[34]
Singularity
At the center of a black hole lies the singularity, where matter is crushed to infinite density, the pull of gravity is infinitely strong, and spacetime has infinite curvature.[35] This means that a black hole's mass becomes entirely compressed into a region with zero volume.[36] This zero-volume, infinitely dense region at the center of a black hole is called a gravitational singularity.
The singularity of a non-rotating black hole has zero length, width, and height; a rotating black hole is smeared out to form a ring shape lying in the plane of rotation.[37] The ring still has no thickness and hence no volume.
The appearance of singularities in general relativity is commonly perceived as signaling the breakdown of the theory.[38] 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.[39][40]
Photon sphere
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.[41] 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.
Ergosphere
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. For a rotating black hole this effect becomes 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.[42]
The ergosphere of a black hole is bounded by, the (outer) event horizon on the inside and an oblate spheroid, which coincides with the event horizon at the poles and is noticeably wider around the equator. The outer boundary is sometimes called the ergosurface.
Objects and radiation can escape normally from the ergosphere. In fact 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 it to slow down
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