A Derivation of the Kerr Metric by Ellipsoid Coordinate Transformation

Einstein's general relativistic eld equation is a nonlinear partial dierential equation that lacks an easy way to obtain exact solutions. The most famous examples are Schwarzschild and Kerr's black hole solutions. The Kerr metric has astrophysical meaning because most of cosmic celestial bodies are rotating. The Kerr metric is even more diffcult to derive than the Schwarzschild metric specically due to off-diagonal term of metric tensor. In this paper, a derivation of Kerr metric was obtained by ellipsoid coordinate transformation, which causes elimination a large amount of tedious derivation. This derivation is not only physics enlightening, but also further deducing some characteristics of the rotating black hole.