The coordinate transformation from Boyer-Lindquist coordinates r, $theta$, $phi$ to cartesian coordinates x, y, z is given by

$\{x\}\; =\; sqrt\; \{r^2\; +\; a^2\}\; sinthetacosphi$

$\{y\}\; =\; sqrt\; \{r^2\; +\; a^2\}\; sinthetasinphi$

$\{z\}\; =\; r\; costheta\; quad$

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.