A black hole is a region of spacetime in which gravity is sufficiently strong that, according to general relativity, there is an event horizon beyond which no future directed signal can reach distant observers. The defining feature is not simply that an object has extremely high density or that it exerts an unusually strong Newtonian gravitational force.
A black hole is a spacetime configuration containing a causal boundary, the event horizon, separating events that can communicate with distant future infinity from those that cannot. For a nonrotating, uncharged black hole described by the Schwarzschild solution, the event horizon occurs at a radius called the Schwarzschild radius, given by two times the gravitational constant times the mass divided by c squared. For a black hole of one solar mass, this radius is approximately 3 kilometres. Real astrophysical black holes can rotate and may possess negligible net electric charge, so the more general Kerr solution is usually more relevant to astrophysics.
The word black refers to the fact that classical general relativity predicts that electromagnetic radiation cannot escape from inside the event horizon to a distant observer. A black hole is therefore not ordinarily visible by light emitted from its interior. Nevertheless, black holes can be detected indirectly through their effects on surrounding matter, stars, radiation and gravitational waves. Gas falling toward a black hole can form a hot accretion disc and emit intense electromagnetic radiation before crossing the horizon.
A black hole can also reveal itself through gravitational effects on companion stars or through gravitational lensing. Merging black holes produce gravitational waves that can be detected by interferometers. The absence of direct light from the horizon does not make black holes hypothetical. Multiple independent observational methods provide evidence for stellar mass, intermediate mass and supermassive black hole populations.
Black holes arise as solutions to Einstein's field equations. The simplest exact solution is the Schwarzschild solution, derived by Karl Schwarzschild in 1916 shortly after general relativity was published. It describes the exterior spacetime around a static, spherically symmetric, uncharged mass. Rotating black holes are described by the Kerr solution, while charged rotating black holes are described mathematically by the Kerr Newman solution.
Astrophysical black holes are expected to be described approximately by the Kerr geometry outside their horizons because they should rapidly lose electromagnetic charge through interactions with surrounding plasma. The classical no hair principle expresses the idea that a stationary black hole in general relativity is characterised externally by a small set of parameters, conventionally mass, angular momentum and electric charge. This is a striking simplification compared with the complicated matter distributions that may have produced the black hole.
The event horizon is not a solid surface. An astronaut freely falling through the horizon of a sufficiently large black hole would not necessarily encounter a locally detectable physical wall at the horizon. The horizon is instead a causal boundary defined by the global structure of spacetime. Once an object passes inward through the event horizon, every future directed path available to it remains within the black hole's interior and cannot reach distant external observers.
For a nonrotating classical black hole, the central region contains a singularity in the mathematical solution, where curvature invariants become divergent and classical general relativity is expected to cease providing a complete physical description. The singularity should not automatically be interpreted as a literal point of infinite density that is known to exist physically. Rather, it indicates that the classical theory reaches a regime where quantum gravity is expected to become important.
Black holes are commonly classified by mass and astrophysical origin. Stellar mass black holes generally form from the collapse of massive stars or through related processes involving binary evolution and mergers. Supermassive black holes occupy the centres of most massive galaxies and have masses ranging from millions to billions of solar masses. Their origins and growth remain major subjects of astrophysical research, involving possibilities such as the growth of early massive seeds, repeated mergers and prolonged accretion.
Intermediate mass black holes occupy a proposed middle range and are being investigated through candidate observations and dynamical evidence. Primordial black holes are hypothetical black holes that could have formed in the early universe from unusually dense regions, although their existence and contribution to dark matter remain unestablished. These categories refer primarily to mass and formation scenarios rather than to fundamentally different laws of gravity.
Black holes have several observable environments. An isolated black hole may be difficult to detect because it emits little or no ordinary electromagnetic radiation directly. A black hole in a binary system can accrete gas from a companion, producing X rays and other radiation as the material becomes compressed and heated. At galactic centres, supermassive black holes can power active galactic nuclei when substantial amounts of matter accrete through a luminous disc and relativistic jets.
Stellar orbits around invisible massive objects can also reveal the presence of a black hole. The centre of the Milky Way contains Sagittarius A star, a supermassive compact object whose mass has been measured through stellar orbital dynamics and other observations. The Event Horizon Telescope has also produced horizon scale images of the emission surrounding M87 star and Sagittarius A star, providing observational views of the shadow like structures associated with their strongly curved spacetimes.
Black holes have unusual effects on time, light and matter because their surrounding spacetime can be extremely curved. Gravitational time dilation becomes strong near the horizon, and light travelling near a black hole can be strongly deflected by gravitational lensing. Matter in an accretion disc can reach enormous temperatures and radiate intensely before crossing the horizon. Rotating black holes can also exhibit frame dragging, in which spacetime itself is influenced by the black hole's angular momentum.
In the Kerr geometry, the region outside the event horizon includes an ergosphere where no observer can remain stationary relative to infinity in the ordinary sense. Energy can in principle be extracted from a rotating black hole through processes related to this rotational energy, including the Penrose process and astrophysical mechanisms associated with magnetic fields and accretion flows.
Black holes occupy an important position at the intersection of general relativity, quantum theory and observational astronomy. Classical general relativity predicts horizons and singularities, while quantum field theory in curved spacetime predicts Hawking radiation, implying that black holes are not completely black when quantum effects are included. Hawking radiation is expected to be extremely weak for astrophysical black holes, making direct observation difficult. Black holes also raise deep questions about entropy, information and the relationship between gravity and quantum mechanics.
Observationally, gravitational wave detections have established a population of merging stellar mass black holes, while stellar dynamics, accretion observations and horizon scale imaging provide independent evidence for supermassive black holes. A black hole is therefore best understood not as an ordinary dark object sitting in space, but as a region of curved spacetime whose causal structure prevents escape beyond its event horizon.
