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2012

On extreme Kerr-throats and zero temperature black-holes

Reiris, Martin

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Recently it was shown that the area A and the angular momentum J of any apparent horizon on a maximal, axisymmetric and asymptotically flat Cauchy hyper-surface of a vacuum space-time satisfy necessarily the universal inequality A >= 8 pi |J|.

We show here that the equality A=8 pi |J| is never attained.
As equality is reached (on globally different data sets) when and only when the surface is an extreme Kerr-throat sphere which has zero "temperature", then our statement could be rephrased following this thermodynamic heuristic as the non-existence of apparent horizons of zero temperature.
We study too the global structure of data sets having surfaces with A=8 pi |J|.

On extreme Kerr-throats and zero temperature black-holes · Around

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A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order
N. Aronszajn · 1957
Earlier work this paper cites.
The Cauchy problem
Yvonne Choquet-Bruhat and James W. York, Jr · 1980
Earlier work this paper cites.
Embedded minimal surfaces, exotic spheres, and manifolds with positive Ricci curvature
William Meeks, III, Leon Simon, and Shing Tung Yau · 1982
Earlier work this paper cites.
Lectures on geometric measure theory
Leon Simon · 1983
Earlier work this paper cites.
General relativity
Robert M. Wald · 1984
Earlier work this paper cites.

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