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September 2013 A geometric theory of zero area singularities in general relativity
Hubert L. Bray, Jeffrey L. Jauregui
Asian J. Math. 17(3): 525-560 (September 2013).

Abstract

The Schwarzschild spacetime metric of negative mass is well-known to contain a naked singularity. In a spacelike slice, this singularity of the metric is characterized by the property that nearby surfaces have arbitrarily small area. We develop a theory of such "zero area singularities" in Riemannian manifolds, generalizing far beyond the Schwarzschild case (for example, allowing the singularities to have nontrivial topology). We also define the mass of such singularities. The main result of this paper is a lower bound on the ADM mass of an asymptotically at manifold of nonnegative scalar curvature in terms of the masses of its singularities, assuming a certain conjecture in conformal geometry. The proof relies on the Riemannian Penrose inequality. Equality is attained in the inequality by the Schwarzschild metric of negative mass. An immediate corollary is a version of the positive mass theorem that allows for certain types of incomplete metrics.

Citation

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Hubert L. Bray. Jeffrey L. Jauregui. "A geometric theory of zero area singularities in general relativity." Asian J. Math. 17 (3) 525 - 560, September 2013.

Information

Published: September 2013
First available in Project Euclid: 8 November 2013

zbMATH: 1282.53059
MathSciNet: MR3119798

Subjects:
Primary: 53C20, 53C80, 83C99

Rights: Copyright © 2013 International Press of Boston

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Vol.17 • No. 3 • September 2013
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