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

Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, D-07743 Jena, Germany
Ansorg, Marcus;
Department of Mathematics and Statistics, University of Otago, PO Box 56, Dunedin 9054, New Zealand
Hennig, Jörg

We investigate the interior hyperbolic region of axisymmetric and stationary black holes surrounded by a matter distribution. First, we treat the corresponding initial value problem of the hyperbolic Einstein equations numerically in terms of a single-domain fully pseudo-spectral scheme. Thereafter, a rigorous mathematical approach is given, in which soliton methods are utilized to derive an explicit relation between the event horizon and an inner Cauchy horizon. This horizon arises as the boundary of the future domain of dependence of the event horizon. Our numerical studies provide strong evidence for the validity of the universal relation A + A − = (8π J ) 2 where A + and A − are the areas of event and inner Cauchy horizon respectively, and J denotes the angular momentum. With our analytical considerations we are able to prove this relation rigorously.


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