The astrophysical processes leading to the creation of black holes.Black hole formation is the astrophysical process by which a black hole is created. The most common pathway is the gravitational collapse of a massive star at the end of its life. When a star with more than about 20 solar masses exhausts its nuclear fuel, it can no longer support itself against gravity, and its core collapses. If the core's mass exceeds the Tolman-Oppenheimer-Volkoff limit (about 2-3 solar masses), no known force can halt the collapse, and a black hole forms. Other pathways include the merger of two neutron stars, which can produce a black hole if the combined mass exceeds the limit, and the direct collapse of gas clouds in the early universe, which may produce supermassive black holes.
The theoretical possibility of black holes was predicted by general relativity in 1915, with Karl Schwarzschild finding the first exact solution in 1916. The specific astrophysical process of stellar collapse to a black hole was worked out in the 1930s by J. Robert Oppenheimer and Hartland Snyder, who showed that a sufficiently massive star would inevitably collapse to a point.
The collapse proceeds when the pressure from nuclear fusion can no longer counteract the inward pull of gravity. The core implodes in milliseconds, reaching densities comparable to nuclear matter. If the resulting neutron star is too massive, it continues to collapse. General relativity predicts that once matter is compressed within its Schwarzschild radius, it inevitably forms a singularity, an object with an event horizon from which nothing, not even light, can escape. The newly formed black hole is initially characterized by its mass and spin, which are determined by the properties of the collapsing star or merging objects.
Understanding black hole formation is crucial for interpreting gravitational wave signals from merging black holes, for modeling the evolution of galaxies (which harbor supermassive black holes at their centers), and for studying the most extreme states of matter in the universe.
The first direct detection of gravitational waves in 2015 was from the merger of two black holes, providing the first direct evidence that black holes exist in binary systems and merge.
| r | variable | radial coordinate — radial coordinate metre |
| a | variable | specific angular momentum (spin parameter) — angular momentum per unit mass metre |
| Δ | variable | horizon function — horizon function metre squared |
| Δ' | variable | derivative of horizon function with respect to r — derivative of horizon function metre |
| ξ | variable | critical impact parameter (azimuthal) — impact parameter metre |
| η | variable | critical impact parameter (polar) — impact parameter metre squared |
| d/dr | operator | computes the rate of change of Δ with respect to r — derivative operator |



