Abstract
It is proven that K-causality coincides with stable causality, and that in a K-causal spacetime the relation K + coincides with the Seifert’s relation. As a consequence the causal relation “the spacetime is strongly causal and the closure of the causal relation is transitive” stays between stable causality and causal continuity.
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References
Akolia G.M., Joshi P., Vyas U.: On almost causality. J. Math. Phys. 22, 1243–1247 (1981)
Bernal A.N., Sánchez M.: Globally hyperbolic spacetimes can be defined as ‘causal’ instead of ‘strongly causal’. Class. Quant. Grav. 24, 745–749 (2007)
Dowker H.F., Garcia R.S., Surya S.: K-causality and degenerate spacetimes. Class. Quant. Grav. 17, 4377–4396 (2000)
Hawking S.W., Ellis G.F.R.: The Large Scale Structure of Space-Time. Cambridge University Press, Cambridge (1973)
Hawking S.W., Sachs R.K.: Causally continuous spacetimes. Commun. Math. Phys. 35, 287–296 (1974)
Janardhan S., Saraykar R.V.: K-causal structure of space-time in general relativity. Pramana-Journal of Physics 70, 587–601 (2008)
Minguzzi E.: The causal ladder and the strength of K-causality. I. Class. Quant. Grav. 25, 015009 (2008)
Minguzzi E.: The causal ladder and the strength of K-causality. II. Class. Quant. Grav. 25, 015010 (2008)
Minguzzi, E.: Chronological spacetimes without lightlike lines are stably causal. Preprint: available at http://arxiv.org/abs/0806.0153v1[gr-qc], 2008, to appear in Commun. Math. Phys. doi:10.1007/s00220-009-0784-6
Minguzzi E.: Limit curve theorems in Lorentzian geometry. J. Math. Phys. 49, 092501 (2008)
Minguzzi E.: Non-imprisonment conditions on spacetime. J. Math. Phys. 49, 062503 (2008)
Minguzzi E.: Weak distinction and the optimal definition of causal continuity. Class. Quant. Grav. 25, 075015 (2008)
Minguzzi, E., Sánchez, M.: The causal hierarchy of spacetimes. In: Baum, H., Alekseevsky, D. (eds.), Recent developments in pseudo-Riemannian geometry, of ESI Lect. Math. Phys., Zurich: Eur. Math. Soc. Publ. House, 2008, pp. 299–358
Seifert H.: The causal boundary of space-times. Gen. Rel. Grav. 1, 247–259 (1971)
Senovilla J.M.M.: Singularity theorems and their consequences. Gen. Rel. Grav. 30, 701–848 (1998)
Sorkin R.D., Woolgar E.: A causal order for spacetimes with C 0 Lorentzian metrics: proof of compactness of the space of causal curves. Class. Quant. Grav. 13, 1971–1993 (1996)
Woodhouse N.M.J.: The differentiable and causal structures of space-time. J. Math. Phys. 14, 495–501 (1973)
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Communicated by G.W. Gibbons
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Minguzzi, E. K-Causality Coincides with Stable Causality. Commun. Math. Phys. 290, 239–248 (2009). https://doi.org/10.1007/s00220-009-0794-4
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DOI: https://doi.org/10.1007/s00220-009-0794-4