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The C-Boundary Construction of SpaceTimes: Application to Stationary Kerr SpaceTime

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Recent Trends in Lorentzian Geometry

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

Abstract

The aim of this chapter is twofold. First, we review several results about the c-boundary of space-times and other boundaries in differential geometry, completing some points which were suggested in the original works. Second, we are going to apply these results to provide a precise description of the c-boundary of the stationary part of (slow rotating) Kerr space time.

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Notes

  1. 1.

    We will use typical background and terminology in Lorentzian geometry as in [2, 15, 16].

  2. 2.

    This section is the development of a seminal idea by Prof. Miguel Sánchez (see also [17]).

  3. 3.

    In this proposition, by the term “Busemann completion,” we must understand the usual Busemann completion up to its asymptotic region,that is, those points of the Busemann boundary associated to curves with diverging radial component.

  4. 4.

    For simplicity, the elements \([x] \in [-6, 6]/R\) will be denoted by x.

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Acknowledgements

The authors acknowledge Prof. Miguel Sánchez the valuable supervision of this work, and the comments by the referee. The authors are partially supported by the Spanish MICINN Grant MTM2010-18099 and Regional J. Andalucía Grant P09-FQM-4496, both with FEDER funds.

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Authors and Affiliations

  1. Departamento de Álgebra, Geometría y Topología, Facultad de Ciencias, Universidad de Málaga, Campus Teatinos, 29071, Málaga, Spain

    J. L. Flores & J. Herrera

Authors
  1. J. L. Flores
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  2. J. Herrera
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Corresponding author

Correspondence to J. Herrera .

Editor information

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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Flores, J.L., Herrera, J. (2012). The C-Boundary Construction of SpaceTimes: Application to Stationary Kerr SpaceTime. 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_11

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