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Hyperbolic Metrics on Riemann Surfaces and Space-Like CMC-1 Surfaces in de Sitter 3-Space Read chapter Read first chapter

2013 | OriginalPaper | Chapter

Stability of Marginally Outer Trapped Surfaces and Applications

Author : Marc Mars

Published in: Recent Trends in Lorentzian Geometry

Publisher: Springer New York

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Abstract

Marginally outer trapped surfaces (MOTS) are special types of codimension-two space-like surfaces in Lorentzian space-times defined by the vanishing of one of its future null expansions. Such surfaces play an important role in gravitational theory as indicators of strong gravitational fields and share some of the properties of minimal hypersurfaces, in particular the existence of a useful notion of stability. In this contribution I describe this notion and present some of its consequences. In particular I will summarize the implications of stability on the topology of MOTS, their role as barriers, the interplay between stability and space–times symmetries and the stability of Killing horizons.

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previous chapter Umbilical-Type Surfaces in SpaceTime
next chapter Area Inequalities for Stable Marginally Trapped Surfaces
Footnotes
1
This result states, roughly speaking, that if two null hypersurfaces touch each other at p and satisfy the property that, locally near p, the hypersurface lying to the past has non-negative null expansion while the one lying to the future has non-positive null expansion, then the two null hypersurfaces must coincide in a neighbourhood of p. The precise statement can be found in Theorems 2.1 and 3.4 in [24].
 
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Metadata
Title
Stability of Marginally Outer Trapped Surfaces and Applications
Author
Marc Mars
Copyright Year
2013
Publisher
Springer New York
Book
Recent Trends in Lorentzian Geometry

Print ISBN: 978-1-4614-4896-9

Electronic ISBN: 978-1-4614-4897-6

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-1-4614-4897-6_4

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