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A geometric theory of zero area singularities in general relativity

Publication ,  Journal Article
Bray, HL; Jauregui, JL
Published in: Asian Journal of Mathematics
2013

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 dene 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 [9]. 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. © 2013 International Press.

Duke Scholars

Published In

Asian Journal of Mathematics

DOI

ISSN

1093-6106

Publication Date

2013

Volume

17

Issue

3

Start / End Page

525 / 560

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0101 Pure Mathematics
 

Citation

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Chicago
ICMJE
MLA
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Bray, H. L., & Jauregui, J. L. (2013). A geometric theory of zero area singularities in general relativity. Asian Journal of Mathematics, 17(3), 525–560. https://doi.org/10.4310/AJM.2013.v17.n3.a6
Bray, H. L., and J. L. Jauregui. “A geometric theory of zero area singularities in general relativity.” Asian Journal of Mathematics 17, no. 3 (2013): 525–60. https://doi.org/10.4310/AJM.2013.v17.n3.a6.
Bray HL, Jauregui JL. A geometric theory of zero area singularities in general relativity. Asian Journal of Mathematics. 2013;17(3):525–60.
Bray, H. L., and J. L. Jauregui. “A geometric theory of zero area singularities in general relativity.” Asian Journal of Mathematics, vol. 17, no. 3, 2013, pp. 525–60. Scival, doi:10.4310/AJM.2013.v17.n3.a6.
Bray HL, Jauregui JL. A geometric theory of zero area singularities in general relativity. Asian Journal of Mathematics. 2013;17(3):525–560.

Published In

Asian Journal of Mathematics

DOI

ISSN

1093-6106

Publication Date

2013

Volume

17

Issue

3

Start / End Page

525 / 560

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0101 Pure Mathematics