An exact solution of the Einstein field equations that is the metric outside a spinning sphere found by Kerr (1963). It was initially not possible to show that this solution fit smoothly with an exact interior solution. Cohen (1967) found a solution for a thin rotating spherical shell which is valid both inside and outside to lowest order in the rotation angular frequency and all orders in the shell mass and which satisfies the correct continuity conditions (Weinberg 1972, p. 241). However, the fact that Kerr's solution was unique and complete was subsequently demonstrated (Shapiro and Teukolsky 1983, p. 338).
Black Hole, Einstein Field Equations, Kerr-Newman Black Hole
References
Boyer, R. H. and Lindquist, R. W. "Maximal Analytic Extension of the Kerr Metric." J. Math. Phys. 8, 265-281, 1967.
Cohen, J. M. In Relativity Theory and Astrophysics, Vol. 1: Relativity and Cosmology (Ed. J. Ehlers). Providence, Amer. Math. Soc., p. 200, 1967.
Kerr, R. P. "Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics." Phys. Rev. Let. 11, 237-238, 1963.
Shapiro, S. L. and Teukolsky, S. A. "Kerr Black Holes." §12.7 in Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects. New York: Wiley, pp. 357-364, 1983.
Weinberg, S. Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. New York: Wiley, pp. 240-241, 1972.
