An event horizon is the boundary around a black hole beyond which no information or matter can escape.The boundary of a black hole from which not even light can escape. Like the edge of a waterfall: as you approach, the boat can still row, but beyond a certain line the current relentlessly carries it down. Here the falling speed of spacetime equals the speed of light.
The first solution of Einstein's equations containing a horizon was found by Karl Schwarzschild in 1916. Initially it was considered a mathematical fiction, but in 1939 Oppenheimer and Snyder showed the reality of gravitational collapse. Key discoveries in singularity theory and horizon properties were made by Roger Penrose and Stephen Hawking in the 1960s-70s. Jacob Bekenstein and Hawking linked the horizon to thermodynamics, proving that black holes have entropy and temperature.
According to Einstein's equations, a massive body curves spacetime. During collapse, a region forms where light cones tilt inward, and any path leads to the singularity. At the horizon, the coordinate singularity of the Schwarzschild metric disappears in suitable coordinates (e.g., Kruskal–Szekeres). Quantum effects near the horizon lead to Hawking radiation, with its temperature and entropy related to the horizon area by the Bekenstein–Hawking formulas.
The Sun, compressed into a black hole, would have a horizon only 6 kilometers in diameter. Earth would continue to move in the same orbit, but eternal darkness and cold would set in.
| r_s | variable | Schwarzschild radius — radius metre |
| M | variable | Mass of the black hole — mass kilogram |
| G | constant | Constant of gravitation in Newton's law — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| c | constant | Speed of light in vacuum — speed of light = 299792458 metre per second |
| v | variable | null coordinate (e.g., advanced time) — null coordinate metre |
| r | variable | radial coordinate — radial coordinate metre |
| ∂_v | operator | differentiates with respect to the null coordinate — partial derivative |
| k | variable | comoving wavenumber — wavenumber reciprocal metre |
| a | variable | scale factor — scale factor |
| H | variable | Hubble parameter — hubble parameter reciprocal second |
| M_{\text{Hill}} | variable | Hill mass limit — mass kilogram |
| R_p | variable | Planet radius — radius metre |
| M_p | variable | Planet mass — mass kilogram |







