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

G. W. Gibbons·G. Holzegel
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Abstract

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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G. W. Gibbons, G. Holzegel. 2006-06-27. The Positive Mass and Isoperimetric Inequalities for Axisymmetric Black Holes in four and five dimensions. https://doi.org/10.1088/0264-9381%2F23%2F22%2F022

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