Kerr metric

The Kerr metric is an exact solution to Einstein’s field equations describing the vacuum spacetime around a rotating, uncharged mass. Its rotation gives spacetime frame dragging and an ergoregion.

Frame dragging: A relativistic effect in which rotating matter drags nearby inertial frames around with it. The Kerr metric quantifies frame dragging caused by the central mass’s angular momentum.
Einstein field equations: The equations of general relativity relating spacetime curvature to matter and energy. The Kerr metric is an exact vacuum solution of these equations.
Black hole: A region of spacetime bounded by an event horizon from which nothing can escape to distant observers. Astrophysical black holes are commonly modeled by the Kerr solution when spin matters.
Roy Kerr: A New Zealand mathematician who discovered the rotating vacuum solution to Einstein’s equations in 1963. Kerr found the metric that now bears his name.
Event horizon: A boundary in spacetime beyond which events cannot influence distant observers. The Kerr solution has an outer event horizon whose radius depends on mass and spin.
Vacuum solution: A spacetime solution of Einstein’s equations in a region where the stress-energy tensor vanishes. Outside the idealized rotating source, Kerr describes vacuum spacetime.
Black hole spin: The angular momentum of a black hole, often expressed relative to its mass. Spin is the parameter that distinguishes Kerr geometry from the nonrotating Schwarzschild case.
Kerr–Schild coordinates: Coordinates expressing certain exact solutions as a flat metric plus a null-vector term. The Kerr solution’s discovery was facilitated by its Kerr–Schild form.
Ergosphere: A region outside a rotating black hole’s event horizon where no observer can remain stationary relative to infinity. The Kerr metric’s frame dragging makes this region unavoidable for stationary observers.
Boyer–Lindquist coordinates: A coordinate system commonly used to express the Kerr spacetime in a form adapted to its symmetries. This coordinate chart makes Kerr’s stationary and axial symmetries explicit.

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