Definitions

# 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, $theta$, $phi$ to cartesian coordinates x, y, z is given by

$\left\{x\right\} = sqrt \left\{r^2 + a^2\right\} sinthetacosphi$
$\left\{y\right\} = sqrt \left\{r^2 + a^2\right\} sinthetasinphi$
$\left\{z\right\} = r costheta quad$

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

## 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.
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