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Stability of Marginally Outer Trapped Surfaces and Applications

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Recent Trends in Lorentzian Geometry

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 26))

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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Notes

  1. 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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Acknowledgements

Financial support under the projects FIS2009- 07238 (Spanish MEC) and P09-FQM-4496 (Junta de Andalucía and FEDER funds) are acknowledged.

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Authors and Affiliations

  1. Departamento de Física Fundamental and Instituto de Física Fundamentaly Matemáticas (IUFFyM), Universidad de Salamanca, Plaza de la Merced s/n, 37008, Salamanca, Spain

    Marc Mars

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Correspondence to Marc Mars .

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Editors and Affiliations

  1. , Dept of Geometry and Topology, University of Granada, Campus Fuentenueva s/n, Granada, E18071, Granada, Spain

    Miguel Sánchez

  2. Departamento de Mátematica Aplicada, Universidad de Granada, Campus de Fuentenueva, Granada, 18071, Spain

    MIguel Ortega

  3. , Dept. of Geometry and Topology, University of Granada, Campus Fuentenueva s/n, Granada, E-18071, Granada, Spain

    Alfonso Romero

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Mars, M. (2012). Stability of Marginally Outer Trapped Surfaces and Applications. In: Sánchez, M., Ortega, M., Romero, A. (eds) Recent Trends in Lorentzian Geometry. Springer Proceedings in Mathematics & Statistics, vol 26. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4897-6_4

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