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Geometric Characterizations of the Kerr Isolated Horizon

Jerzy Lewandowski·Tomasz Pawlowski
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Abstract

We formulate conditions on the geometry of a non-expanding horizon $Δ$ which are sufficient for the space-time metric to coincide on $Δ$ with the Kerr metric. We introduce an invariant which can be used as a measure of how different the geometry of a given non-expanding horizon is from the geometry of the Kerr horizon. Directly, our results concern the space-time metric at $\IH$ at the zeroth and the first orders. Combained with the results of Ashtekar, Beetle and Lewandowski, our conditions can be used to compare the space-time geometry at the non-expanding horizon with that of Kerr to every order. The results should be useful to numerical relativity in analyzing the sense in which the final black hole horizon produced by a collapse or a merger approaches the Kerr horizon.

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Jerzy Lewandowski, Tomasz Pawlowski. 2001-12-18. Geometric Characterizations of the Kerr Isolated Horizon. https://doi.org/10.1142/s0218271802001986

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