Kerr metric - Definition and Overview

In physics, he Kerr metric describes the geometry of spacetime around a rotating black hole. It is a metric, discovered in 1963, which is an exact solution to the Einstein field equations.

The Boyer-Lindquist form of the line element is given by

<math>ds^2=\rho^2(\frac{dr^2}{\Delta}+d\theta^2)+(r^2+a^2)\sin^2\theta d\phi^2-dt^2+\frac{2mr}{\rho^2}(a\sin^2\theta d\phi-dt)^2<math>

where

ρ²=r² + a²cos²θ

and

Δ=r² - 2mr + a².

Here m is the mass of the black hole, and a is the angular velocity, as measured by a distant observer. Note that r does not agree with the radial coordinate of the Schwarzschild solution, except asymptotically.