Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2011-03-23
J.Phys.Conf.Ser.314:012017,2011
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Proceedings of the Spanish Relativity Meeting ERE 2010, 10 pages, 5 figures
Scientific paper
10.1088/1742-6596/314/1/012017
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 $\Ap\Am = (8\pi J)^2$ where $\Ap$ and $\Am$ 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.
Ansorg Marcus
Hennig Jörg
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