A Beemian sampler: 1966–2002

Ehrlich, Paul E.; Easley, Kevin L.

doi:10.1090/conm/359/06552

Cited by 1 publication

(4 citation statements)

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“…Clarke (1971) showed that strongly causal spacetimes could be made lightlike geodesically complete through a conformal change of metric and Seifert (1971) showed that under stable causality it could also be made causally geodesically complete. From the causal point of view the optimal result in this direction was obtained by Beem with the following theorem (Beem et al 1996;Ehrlich and Easley 2004) that implies the results by Clarke and Seifert.…”

Section: Theorem 439 Let H Be An Auxiliary Riemannian Metric a Spacmentioning

confidence: 71%

“…The important role of causal disconnection in Hawking and Penrose's theorem was stressed by Beem et al (1996) (see also Beem and Ehrlich 1977;Ehrlich and Easley 2004).…”

Section: Hawking and Penrose's Theorem And Borde's Theoremmentioning

confidence: 97%

“…We have also the following result whose proof is obtained from the previous one by replacing p with S, and maximizing with S-maximizing. The following concept, first introduced in Beem et al (1996) (see also Beem and Ehrlich 1977;Ehrlich and Easley 2004), will play an important role in the study of Hawking and Penrose's singularity theorem.…”

Section: Theorem 264 Let (M G) Be Non-totally Imprisoning For Evermentioning

confidence: 99%

“…The notions of null, timelike, spacelike geodesic completeness are mutually independent (Beem 1976b;Ehrlich and Easley 2004). The stability of completeness and incompleteness was studied by Beem and Ehrlich (Lerner 1973;Beem and Ehrlich 1987;Beem et al 1996;Beem 1997).…”

Section: The Geometry Of Geodesic Congruencesmentioning

confidence: 99%

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Lorentzian causality theory

Minguzzi

2019

Living Rev Relativ

157

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I review Lorentzian causality theory paying particular attention to the optimality and generality of the presented results. I include complete proofs of some foundational results that are otherwise difficult to find in the literature (e.g. equivalence of some Lorentzian length definitions, upper semi-continuity of the length functional, corner regularization, etc.). The paper is almost self-contained thanks to a systematic logical exposition of the many different topics that compose the theory. It contains new results on classical concepts such as maximizing curves, achronal sets, edges, horismos, domains of dependence, Lorentzian distance. The treatment of causally pathological spacetimes requires the development of some new versatile causality notions, among which I found particularly convenient to introduce: biviability, chronal equivalence, araying sets, and causal versions of horismos and trapped sets. Their usefulness becomes apparent in the treatment of the classical singularity theorems, which is here considerably expanded in the exploration of some variations and alternatives.

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Section: Theorem 439 Let H Be An Auxiliary Riemannian Metric a Spacmentioning

confidence: 71%

“…The important role of causal disconnection in Hawking and Penrose's theorem was stressed by Beem et al (1996) (see also Beem and Ehrlich 1977;Ehrlich and Easley 2004).…”

Section: Hawking and Penrose's Theorem And Borde's Theoremmentioning

confidence: 97%

Section: Theorem 264 Let (M G) Be Non-totally Imprisoning For Evermentioning

confidence: 99%