Journal ArticleDOI
Stable minimal surfaces and spatial topology in general relativity
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This article is published in Mathematische Zeitschrift.The article was published on 1982-09-01. It has received 9 citations till now. The article focuses on the topics: Four-force & Introduction to the mathematics of general relativity.read more
Citations
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On the topology of stationary black holes
TL;DR: In this paper, it was shown that the domain of outer communication of a stationary, globally hyperbolic spacetime satisfying the null energy condition must be simply connected under suitable additional hypotheses.
Journal ArticleDOI
On the topology of stationary black holes
TL;DR: In this paper, it was shown that the domain of outer communication of a stationary, globally hyperbolic spacetime satisfying the null energy condition must be simply connected under suitable additional hypotheses.
Journal ArticleDOI
On the topology of black holes
TL;DR: In this article, it was shown that the surface of a black hole must have 2-sphere topology and that the topology of space in its vicinity is simple, which is the same as that of a 2-dimensional Euclidean plane.
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Uniqueness of a static charged dilaton black hole
TL;DR: In this article, the uniqueness of a static charged dilaton black hole related to low-energy string theory was proved by exploiting the Lichnerowicz identity of spinors satisfying the Dirac equation.
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The topology of asymptotically Euclidean static perfect fluid space-time
TL;DR: In this paper, it was shown that a geodesically complete, asymptotically Euclidean, static perfect fluid space-time satisfying the time-like convergence condition and having a connected fluid region is diffeomorphic to ℝ3×ℝ.
References
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Embedded minimal surfaces, exotic spheres, and manifolds with positive Ricci curvature
TL;DR: In this article, it was shown that the covering space of any irreducible orientable three-dimensional manifold is irrecoverable, provided the complementary volume is not a standard ball, and provided there exists no embedded one-sided RP2.
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Singularities in nonsimply connected space--times
TL;DR: In this article, it was shown that if the normal geodesics to the spacelike slice are converging on a suitable compact set, and the space-time satisfies a standard energy condition, then it is timelike geodesically incomplete.
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On the topology of spacelike hypersurfaces, singularities, and black holes
TL;DR: In this paper, sufficient topological conditions and some reasonable geometric properties near infinity are given on a partial Cauchy surface to study the occurrence of singularities and the topological structure of smooth event horizons.
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A restriction on the topology of Cauchy surfaces in general relativity
TL;DR: In this paper, it was shown that a part of a Cauchy surface bounded by a uniformly convex sphere is compact and simply connected in globally hyperbolic and geodesically complete space-time.