Boyer–Lindquist coordinates

In the mathematical description of general relativity, the Boyer–Lindquist coordinates are a generalization of the coordinates used for the metric of a Schwarzschild black hole that can be used to express the metric of a Kerr black hole.

The coordinate transformation from Boyer–Lindquist coordinates ${\displaystyle r,\theta }$, ${\displaystyle \phi }$ to Cartesian coordinates x, y, z is given by

The line element for a black hole with mass ${\displaystyle M}$, angular momentum ${\displaystyle J}$, and charge ${\displaystyle Q}$ in Boyer–Lindquist coordinates and natural units (${\displaystyle G=c=1}$) is

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