Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-04-14
Annales Henri Poincare 10:1075-1095,2009
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
21 pages, 1 figure
Scientific paper
10.1007/s00023-009-0012-0
We use soliton methods in order to investigate the interior electrovacuum region of axisymmetric and stationary, electrically charged black holes with arbitrary surrounding matter in Einstein-Maxwell theory. These methods can be applied since the Einstein-Maxwell vacuum equations permit the formulation in terms of the integrability condition of an associated linear matrix problem. We find that there always exists a regular inner Cauchy horizon inside the black hole, provided the angular momentum $J$ and charge $Q$ of the black hole do not vanish simultaneously. Moreover, the soliton methods provide us with an explicit relation for the metric on the inner Cauchy horizon in terms of that on the event horizon. In addition, our analysis reveals the remarkable universal relation $(8\pi J)^2+(4\pi Q^2)^2=A^+ A^-$, where $A^+$ and $A^-$ denote the reas of event and inner Cauchy horizon respectively.
Ansorg Marcus
Hennig Jörg
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