Processes and origins of black hole formation, including mass gaps and evolutionary styles.Black holes form when matter is compressed beyond a critical density, creating a gravitational pull so strong that nothing, not even light, can escape. The most common pathway is the core collapse of a massive star at the end of its life: when nuclear fusion ceases, the star's core can no longer support its own weight and implodes, forming a stellar-mass black hole. However, the process is not uniform — there are 'mass gaps' where black holes of certain masses are rarely observed, suggesting that different formation mechanisms operate in different mass ranges.
The concept of a body from which light cannot escape dates to John Michell in 1783 and Pierre-Simon Laplace in 1796, but the modern theory emerged from Karl Schwarzschild's 1916 solution to Einstein's field equations. The specific formation mechanism via stellar collapse was clarified by J. Robert Oppenheimer and Hartland Snyder in 1939.
The core collapse begins when a star with more than about 8 solar masses exhausts its nuclear fuel. The core, now composed of iron, cannot fuse further and collapses under gravity in milliseconds. 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. For heavier stars, some material is ejected in a supernova, but a remnant black hole remains. Alternative pathways include the direct collapse of very massive stars in the early universe, which may skip the supernova phase, and the merger of two neutron stars, which can produce a black hole if the combined mass exceeds the limit.
Understanding formation mechanisms helps astrophysicists interpret gravitational wave signals from LIGO and Virgo, revealing the masses and spins of merging black holes and testing predictions about mass gaps.
The first direct detection of gravitational waves in 2015 came from the merger of two black holes, each about 30 solar masses — a mass range that was previously unexpected and hinted at formation pathways distinct from ordinary stellar evolution.
| M_{\rm PBH} | variable | mass of the primordial black hole — mass kilogram |
| M_{\rm eq} | variable | horizon mass at matter-radiation equality — mass kilogram |
| T_{\rm eq} | variable | temperature at matter-radiation equality — temperature kelvin |
| T_\star | variable | temperature at formation time — temperature kelvin |
| δM | variable | Infinitesimal change in black hole mass — mass kilogram |
| κ | variable | Surface gravity of the black hole — surface gravity metre per second squared |
| δA | variable | Infinitesimal change in horizon area — area square metre |
| Ω_H | variable | Angular velocity of the horizon — angular velocity radian per second |
| δJ | variable | Infinitesimal change in angular momentum — angular momentum kilogram square metre per second |
| δ | operator | Infinitesimal variation of a quantity — variation |






