The interior of axisymmetric and stationary black holes: Numerical and analytical studies

Marcus Ansorg

We investigate the interior hyperbolic region of axisymmetric and stationary black holes surrounded by a matter distribution. In the first part of the talk we treat the corresponding initial value problem of the hyperbolic Einstein equations numerically in terms of a single-domain pseudo-spectral scheme. A rigorous mathematical approach is given in the second part, in which soliton methods are utilized to derive an explicit relation between the event horizon and an inner Cauchy horizon that arises as the boundary of the future domain of dependence of the event horizon. Both numerical and analytical studies prove the universal relation $A_{\rm EH} A_{\rm CH} = (8\pi J)2$ where $A_{\rm EH}$ and $A_{\rm CH}$ are the areas of event and inner Cauchy horizon respectively, and $J$ denotes the black hole's angular momentum.