An Invitation to Lorentzian Geometry

Survey Article

Abstract

The intention of this article is to give a flavour of some global problems in General Relativity. We cover a variety of topics, some of them related to the fundamental concept of Cauchy hypersurfaces:
  1. (1)

    structure of globally hyperbolic spacetimes,

     
  2. (2)

    the relativistic initial value problem,

     
  3. (3)

    constant mean curvature surfaces,

     
  4. (4)

    singularity theorems,

     
  5. (5)

    cosmic censorship and Penrose inequality,

     
  6. (6)

    spinors and holonomy.

     

Keywords

Global Lorentzian geometry Cauchy hypersurface Global hyperbolicity Einstein equation Initial value problem CMC hypersurface Singularity theorems ADM mass Cosmic censorship hypotheses Penrose inequality Spinors Lorentzian holonomy 

Mathematics Subject Classification

53C50 8306 8302 83C05 83C75 

Notes

Acknowledgements

The second-named author is partially supported by the Grants MTM2010–18099 (MICINN) and P09-FQM-4496 (J. Andalucía) with FEDER funds.

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Copyright information

© Deutsche Mathematiker-Vereinigung and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität RegensburgRegensburgGermany
  2. 2.Departamento de Geometría y Topología, Facultad de CienciasUniversidad de GranadaGranadaSpain

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