MG12 - Talk detail
 

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Abstract

The inner Cauchy horizon of axisymmetric and stationary black holes with surrounding matter in Einstein-Maxwell theory

We study the linear problem for the axisymmetric and stationary Einstein-Maxwell equations in order to investigate the interior electrovacuum region of axisymmetric and stationary, electrically charged black holes with arbitrary surrounding matter in Einstein-Maxwell theory. 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 = AEH*ACH, where AEH and ACH denote the areas of event and inner Cauchy horizon respectively.

Non-existence of stationary two-black-hole configurations

We resume former discussions of the question, whether the spin-spin repulsion and the gravitational attraction of two aligned black holes can balance each other. To answer the question we formulate a boundary value problem for two separate (Killing-) horizons and apply the inverse (scattering) method to solve it. Making use of results of Manko, Ruiz and Sanabria-Gómez and a novel black hole criterion, we prove the non-existence of the equilibrium situation in question.

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