Abstract

Einstein's general relativistic field equation is a nonlinear partial differential equation that lacks an easy way to obtain exact solutions. The most famous of which are Schwarzschild and Kerr's black hole solutions. Kerr metric has astrophysical meaning because most cosmic celestial bodies rotate. Kerr metric is even harder than Schwarzschild metric to be derived directly 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 of large amount of tedious derivation. This derivation is not only physically enlightening, but also further deducing some characteristics of the rotating black hole.

Key words: General relativity, Schwarzschild metric, Kerr metric, ellipsoid coordinate transformation, exact solutions.