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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

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

Authors : J. L. Flores, J. Herrera

Published in: Recent Trends in Lorentzian Geometry

Publisher: Springer New York

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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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previous chapter Can We Make a Finsler Metric Complete by a Trivial Projective Change?
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Footnotes
1
We will use typical background and terminology in Lorentzian geometry as in [2, 15, 16].
 
2
This section is the development of a seminal idea by Prof. Miguel Sánchez (see also [17]).
 
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
For simplicity, the elements \([x] \in [-6, 6]/R\) will be denoted by x.
 
Literature
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Alaña, V., Flores, J.L.: The causal boundary of product spacetimes. Gen. Relat. Gravit. 39(10), 1697–1718 (2007)MATHCrossRef
2.
Beem, J.K., Ehrlich, P.E., Easley, K.L.: Global Lorentzian geometry. In: Monographs Textbooks Pure Appl. Math. vol. 202. Dekker, New York (1996)
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Caponio, E., Javaloyes, M.A., Sánchez, M.: On the interplay between Lorentzian Causality and Finsler metrics of Randers type. Rev. Matem. Iberoamericana 27, 919–952 (2011)MATHCrossRef
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Flores, J.L., Harris, S.G.: Topology of the causal boundary for standard static spacetimes. Class. Quant. Grav. 24(5), 1211–1260 (2007)MathSciNetMATHCrossRef
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Flores, J.L., Herrera, J., Sánchez, M.: On the final definition of the causal boundary and its relation with the conformal boundary. Adv. Theor. Math. Phys. 15(4), 991–1058 (2011) Available at arXiv:1001.3270v3 [math-ph]
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Flores, J.L., Herrera, J., Sánchez, M.: Gromov, Cauchy and causal boundaries for Riemannian, Finslerian and Lorentzian manifolds. Memoirs of the AMS, To appear. Available at arXiv:1011:1154v3 [math.DG]
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Gromov, M.: Metric structures for Riemannian and non-Riemannian spaces. In: Progress in Mathematics, vol. 152. Birkhäuser, Boston (1999)
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Hawking, S.W., Ellis, G.F.R.: The Large Scale Structure of Space-Time. Cambridge University, Cambridge (1973)MATHCrossRef
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Minguzzi, E., Sánchez, M.: The causal hierarchy of spacetimes. In: Recent developments in pseudo-Riemannian Geometry, pp. 299–358 (2008). ESI Lect. in Math. Phys., European Mathematical Society Publishing House. (Available at gr-qc/0609119)
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O’Neill, B.: Semi-Riemannian Geometry with Applications to Relativity. Academic, New York (1983)MATH
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Sánchez, M.: The causal boundary of a spacetime and its relation with the classical Gromov and Cauchy boundaries. Plenary contribution at the Int. Meeting on Differential Geometry, Córdoba, Nov. 15–17, 2010
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Wald, R.M.: General Relativity. University of Chicago Press, Chicago (1984)MATH
Metadata
Title
The C-Boundary Construction of SpaceTimes: Application to Stationary Kerr SpaceTime
Authors
J. L. Flores
J. Herrera
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_11

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