Causal boundaries for general relativistic space-times

Budic, R.; Sachs, Rainer K.

doi:10.1063/1.1666812

Cited by 55 publications

(74 citation statements)

References 5 publications

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“…This result, proposed in [24] in a slightly different context, was proved by Budic and Sachs in [3,Th. 6.2].…”

Section: Causal Ladder and The Boundary Of Spacetimesmentioning

confidence: 71%

“…A conceptually different approach to the causal boundary of spacetimes consists of using identifications instead of pairs to form the ideal points of the boundary (see [9]; and the subsequent papers [23,3,25,26]). This approach presents important objections (see for example [20,Section 2.2] for an interesting discussion); however, sometimes some identifications may be useful to emphasize certain aspects of the original spacetime.…”

Section: Comparison With Other Approachesmentioning

confidence: 99%

“…The procedure proposed in [23], very close to the GKP approach, also fails in simple examples (see [18]). Another approach proposed in [3], and improved later in [25,26] via the Szabados relation (Definition 2.6; see also Section 8), again presents undesirable properties (see [17], [18], [20,Sections 2.2,5]). …”

Section: Introductionmentioning

confidence: 99%

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The Causal Boundary of Spacetimes Revisited

Flores

2007

Commun. Math. Phys.

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Abstract.We present a new development of the causal boundary of spacetimes, originally introduced by Geroch, Kronheimer and Penrose. Given a strongly causal spacetime (or, more generally, a chronological set), we reconsider the GKP ideas to construct a family of completions with a chronology and topology extending the original ones. Many of these completions present undesirable features, like those which appeared in previous approaches by other authors. However, we show that all these deficiencies are due to the attachment of an "excessively big" boundary. In fact, a notion of "completion with minimal boundary" is then introduced in our family such that, when we restrict to these minimal completions, which always exist, all previous objections disappear. The optimal character of our construction is illustrated by a number of satisfactory properties and examples.

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“…This result, proposed in [24] in a slightly different context, was proved by Budic and Sachs in [3,Th. 6.2].…”

Section: Causal Ladder and The Boundary Of Spacetimesmentioning

confidence: 71%

Section: Comparison With Other Approachesmentioning

confidence: 99%

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The Causal Boundary of Spacetimes Revisited

Flores

2007

Commun. Math. Phys.

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“…The second one is to topologize the completion -so that one can check precisely when a sequence or curve in M converges to a point in ∂ c M . These two problems are closely related, and yielded a hard identification problem, studied by many authors shortly after the seminal GKP paper (see, for example, [10,31,47]). The main difficulty for this problem was that, apparently, there were many possible choices of both, identifications and topologies.…”

Section: Causal and Conformal Boundariesmentioning

confidence: 99%

Recent progress on the notion of global hyperbolicity

Plaue¹,

Rendall²,

Scherfner³

2011

Advances in Lorentzian Geometry

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Abstract. Global hyperbolicity is a central concept in Mathematical Relativity. Here, we review the different approaches to this concept explaining both, classical approaches and recent results. The former includes Cauchy hypersurfaces, naked singularities, and the space of the causal curves connecting two events. The latter includes structural results on globally hyperbolic spacetimes, their embeddability in LorentzMinkowski, and the recently revised notions of both causal and conformal boundaries. Moreover, two criteria for checking global hyperbolicity are reviewed. The first one applies to general splitting spacetimes. The second one characterizes accurately global hyperbolicity and spacelike Cauchy hypersurfaces for standard stationary spacetimes, in terms of a naturally associated Finsler metric.

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“…Chronological mappings between causal spaces have been considered many times in the literature (see e.g. [24,8,41,42,28]). …”

Section: Causal Mappings Versus Chronological Relationsmentioning

confidence: 99%

Further properties of causal relationship: causal structure stability, new criteria for isocausality and counterexamples

Gómez-Lobo

Sánchez

2005

Class. Quantum Grav.

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the concept of causal mapping between spacetimes -essentially equivalent in this context to the chronological map one in abstract chronological spaces-, and the related notion of causal structure, have been introduced as new tools to study causality in Lorentzian geometry. In the present paper, these tools are further developed in several directions such as: (i) causal mappings -and, thus, abstract chronological ones-do not preserve two levels of the standard hierarchy of causality conditions (however, they preserve the remaining levels as shown in the above reference), (ii) even though global hyperbolicity is a stable property (in the set of all timeoriented Lorentzian metrics on a fixed manifold), the causal structure of a globally hyperbolic spacetime can be unstable against perturbations; in fact, we show that the causal structures of Minkowski and Einstein static spacetimes remain stable, whereas that of de Sitter becomes unstable, (iii) general criteria allow us to discriminate different causal structures in some general spacetimes (e.g. globally hyperbolic, stationary standard); in particular, there are infinitely many different globally hyperbolic causal structures (and thus, different conformal ones) on R 2 , (iv) plane waves with the same number of positive eigenvalues in the frequency matrix share the same causal structure and, thus, they have equal causal extensions and causal boundaries.

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Causal boundaries for general relativistic space-times

Cited by 55 publications

References 5 publications

The Causal Boundary of Spacetimes Revisited

The Causal Boundary of Spacetimes Revisited

Recent progress on the notion of global hyperbolicity

Further properties of causal relationship: causal structure stability, new criteria for isocausality and counterexamples

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