Abstract
The future completion of a spacetime, equipped with the future chronological topology, is ripe for consideration of constructions and properties typically expressed for a spacetime. Joining elements with a causal curve is problematic, but some progress is reported. We look at trying to do global hyperbolicity in the future completion \(\hat{M}\) of M; this works well if M has a compact Cauchy surface, but otherwise, not so well.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
J.L. Flores, S.G. Harris, Topology of the causal boundary for standard static spacetimes. Class. Quantum Grav. 24, 1211–1260 (2007)
J.L. Flores, J. Herrera, M. Sánchez, Gromov, Cauchy, and Causal Boundaries for Riemannian, Finslerian and Lorentzian Manifolds, vol. 226, no. 1064. (Memoirs American Mathematical Society, 2013)
J.L. Flores, J. Herrera, M. Sánchez, On the final definition of the causal boundary and its relation with the conformal boundary. Adv. Theor. Math. Phys. 15, 991–1057 (2011)
R.P. Geroch, E.H. Kronheimer, R. Penrose, Ideal points in space-time. Proc. Roy. Soc. Lond. A 327, 545–567 (1972)
S.G. Harris, Universality of the future chronological boundary. J. Math. Phys. 39, 5427–5445 (1998)
S.G. Harris, Topology of the future chronological boundary: universality for spacelike boundaries. Class. Quantum Grav. 17, 551–603 (2000)
S.G. Harris, Causal boundary for standard static spacetimes. Nonlinear Anal. 47, 2971–2981 (2001)
S.G. Harris, Discrete group actions on spacetimes. Class. Quantum Grav. 21, 1209–1236 (2004)
S.W. Hawking, G.F.R. Ellis, Large Scale Structure of Space-Time. (Cambridge University Press, Cambridge, 1972)
D. Marolf, S.R. Rolf, A new recipe for causal completion. Class. Quantum Grav. 20, 4085–4117 (2003)
L.B. Szabados, Causal boundary for strongly causal spacetimes. Class. Quantum Grav. 5, 121–134 (1988)
L.B. Szabados, Causal boundary for strongly causal spacetimes II. Class. Quantum Grav. 6, 77–91 (1989)
Acknowledgements
These researches were conducted or commenced at VIII International Meeting on Lorentzian Geometry. The author wishes particularly to thank Miguel Sánchez, José Flores, and Jónatan Herrera for helpful discussions.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Harris, S.(.G. (2017). Future Completion of a Spacetime and Standard Causal Constructions. In: Cañadas-Pinedo, M., Flores, J., Palomo, F. (eds) Lorentzian Geometry and Related Topics. GELOMA 2016. Springer Proceedings in Mathematics & Statistics, vol 211. Springer, Cham. https://doi.org/10.1007/978-3-319-66290-9_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-66290-9_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-66289-3
Online ISBN: 978-3-319-66290-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)