Boyer-Lindquist coordinates

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 r, $θ$ , $φ$ to cartesian coordinates x, y, z is given by

${x} = \sqrt {r^2 + a^2} \sin\theta\cos\phi$

${y} = \sqrt {r^2 + a^2} \sin\theta\sin\phi$

${z} = r \cos\theta \quad$

For a physical interpretation of the parameter a, see the Kerr Metric.

[edit] References

Boyer, R. H. and Lindquist, R. W. Maximal Analytic Extension of the Kerr Metric. J. Math. Phys. 8, 265-281, 1967.
Shapiro, S. L. and Teukolsky, S. A. Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects. New York: Wiley, p. 357, 1983.