On the GKP and BS constructions of the <i>c</i>-boundary

Kuang, Zhiquan; Liang, Canbin

doi:10.1063/1.528032

Cited by 14 publications

(17 citation statements)

References 10 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%

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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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Section: Introductionmentioning

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%

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%

“…In judging a proposed completion, applying our intuition to simple examples is an important source of guidance. Such examples have played an important part in the previous literature on this subject [3,4,6]. We will use several simple toy examples to illustrate the different aspects of the construction as we go along.…”

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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Geodesic connectedness of the causal completion in the Lorentzian geometry

Kim

Yim

2006

Gen Relativ Gravit

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We consider the topology of the BS causal completion, and show that it is not distorted in the causal direction. Using this result, we show that the causal completion with spacelike causal boundary in the sense of the BS construction satisfies the formal definition of the global hyperbolicity. We also show that any two causally related points in the causal completion can be connected by a causal geodesic.

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On the GKP and BS constructions of the c-boundary

Cited by 14 publications

References 10 publications

The Causal Boundary of Spacetimes Revisited

The Causal Boundary of Spacetimes Revisited

A new recipe for causal completions

Geodesic connectedness of the causal completion in the Lorentzian geometry

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