The Positive Mass and Isoperimetric Inequalities for Axisymmetric Black Holes in four and five dimensions

Details The Positive Mass and Isoperimetric Inequalities for Axisymmetric Black Holes in four and five dimensions The Positive Mass and Isoperimetric Inequalities for Axisymmetric Black Holes in four and five dimensions

2006-06-27

arxiv.org/abs/gr-qc/0606116v1

Class.Quant.Grav.23:6459-6478,2006

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

21 pages, 3 figures

Scientific paper

10.1088/0264-9381/23/22/022

In this paper we revisit Brill's proof of positive mass for three-dimensional, time-symmetric, axisymmetric initial data and generalise his argument in various directions. In 3+1 dimensions, we include an apparent horizon in the initial data and prove the Riemannian Penrose inequality in a wide number of cases by an elementary argument. In the case of 4+1 dimensions we obtain the analogue of Brill's formula for initial data admitting a generalised form of axisymmetry. Including an apparent horizon in the initial data, the Riemannian Penrose inequality is again proved for a large class of cases. The results may have applications in numerical relativity.

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