Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2000-12-31
Int.J.Mod.Phys. D11 (2002) 739-746
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
11 pages, relevance of the results for the numerical relativity explained, mistakes corrected
Scientific paper
10.1142/S0218271802001986
We formulate conditions on the geometry of a non-expanding horizon $\Delta$ which are sufficient for the space-time metric to coincide on $\Delta$ 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.
Lewandowski Jerzy
Pawlowski Tomasz
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