<i>c</i>-boundary of Taub’s plane-symmetric static vacuum spacetime

Kuang, Zhiquan; Li, Jianzeng; Liang, Canbin

doi:10.1103/physrevd.33.1533

Cited by 16 publications

(21 citation statements)

References 8 publications

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“…any two points can be separated by neighborhoods. However, this method fails to produce the "expected" completion in some examples [16], [17], [20,Section 5]. On the other hand, although strong separation properties as T 2 are desirable, there are no physical reasons to impose it a priori.…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

The Causal Boundary of Spacetimes Revisited

Flores

2007

Commun. Math. Phys.

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“…This construction allows one to define a topology satisfying the basic requirements above, but it does not always give the expected relations between limits and ideal points in simple examples. Some examples of these difficulties were discussed in [3,4,6], and similar issues arise even in de Sitter space and anti-de Sitter space.…”

Section: Introductionmentioning

confidence: 99%

“…However, this construction fails to produce the 'obvious' completion in some examples [3,4]. Attempts have been made in the past to modify the topology to produce more satisfactory results [5], but these modifications also fail in some examples [6].…”

Section: Introductionmentioning

confidence: 99%

“…There is a smooth function Ω onM such that Ω > 0 and Ω 2 g = θ * (g) on θ(M ), 2. Ω = 0 and dΩ = 0 on ∂M , 3. every null geodesic in M has two endpoints on ∂M .…”

Section: Introductionmentioning

confidence: 99%

“…In the quotient constructions, the topology adopted was essentially that introduced by Geroch, Kronheimer and Penrose [2], perhaps with small refinements 3 . This topology is basically constructed by introducing a suitable 'generalised Alexandrov' topology on the space of all IPs and IFs, and adopting the quotient topology on the spaceM obtained after identifying the members of an equivalence class.…”

Section: Introductionmentioning

confidence: 99%

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A new recipe for causal completions

Marolf

Ross

2003

Class. Quantum Grav.

120

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We discuss the asymptotic structure of spacetimes, presenting a new construction of ideal points at infinity and introducing useful topologies on the completed space. Our construction is based on structures introduced by Geroch, Kronheimer, and Penrose and has much in common with the modifications introduced by Budic and Sachs as well as those introduced by Szabados. However, these earlier constructions defined ideal points as equivalence classes of certain past and future sets, effectively defining the completed space as a quotient. Our approach is fundamentally different as it identifies ideal points directly as appropriate pairs consisting of a (perhaps empty) future set and a (perhaps empty) past set. These future and past sets are just the future and past of the ideal point within the original spacetime. This provides our construction with useful causal properties and leads to more satisfactory results in a number of examples. We are also able to endow the completion with a topology. In fact, we introduce two topologies, which illustrate different features of the causal approach. In both topologies, the completion is the original spacetime together with endpoints for all timelike curves. We explore this procedure in several examples, and in particular for plane wave solutions, with satisfactory results.

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