The Mathematics of Black Holes: Metrics and Horizons

Black holes are described by solutions to Einstein’s equations called metrics.
The Schwarzschild metric models a non-rotating, uncharged black hole.
The Kerr metric extends this to rotating black holes, adding frame-dragging effects.
Horizons mark the boundary where not even light can escape gravity’s pull.
The event horizon acts as a one-way surface—nothing crosses back out.
The singularity at the center is where spacetime curvature becomes infinite.
The Reissner–Nordström metric describes charged black holes.
Hawking radiation suggests black holes slowly evaporate despite their horizons.
Metrics let physicists predict orbits, time dilation, and gravitational lensing near black holes.
At their core, black hole metrics show how geometry itself defines the most extreme objects in the universe.