Black hole

A black hole is a region from whose events no future-directed causal curve can reach the distant exterior. In an asymptotically flat spacetime with future null infinity ${\mathcal{I}}^{+}$, the standard definition isHere $J^{-}$ denotes the causal past and ${\mathcal{H}}^{+}$ is the future event horizon. This is a statement about the complete causal geometry, rather than a material surface or a local force threshold.

For a Schwarzschild black hole, ingoing Eddington-Finkelstein coordinates give outgoing radial null geodesics the slope $dr/dv=(1-2M/r)/2$ in units $G=c=1$. Inside $r=2M$ even this outgoing family moves toward smaller areal radius; the other future radial null family does too. A regular horizon can therefore prevent escape without being a curvature singularity.^[ref]

Rotating examples are described by a Kerr black hole. A dynamically forming event horizon need not coincide with a slice's apparent horizon; locating the former requires global escape information.

A black hole is a region in space where the gravitational pull is so strong that nothing, not even light, can escape from it. This phenomenon occurs when a massive star collapses under its own gravity at the end of its life cycle. Black holes are characterized by three main properties: 1. **Singularity**: At the center of a black hole lies the singularity, a point where gravity is thought to be infinitely strong, and known laws of physics break down.