Black-Hole Thermodynamics and Hawking Radiation

Abstract

The most generally known solution to Einstein’s field equations that contains black holes is that of the Kerr—Newman, family, which describes axisymmetric matter-free spacetimes and represents rotating and electrically charged black holes. This solution is a three-parameter family labelled by total mass energy M, angular momentum J and charge Q. The line element is given by

$$ds^{^2 } = \frac{\Delta } {\Sigma }\left( {dt - a\sin ^2 \theta d\varphi } \right)^2 - \frac{{\sin ^2 \theta }} {\Sigma }\left( {\left( {r^2 + a^2 } \right)d\varphi - adt} \right)^2 - \frac{\Sigma } {\Delta }dr^2 - \Sigma d\theta ^2 $$

((1a))

where

$$\Delta = r^2 + a^2 - 2Mr + Q^2 ;\Sigma = r^2 + a^2 \cos ^2 \theta ;j = Ma $$

((1b))