Singular boundaries of space–times

Geroch, Robert; Liang, Canbin; Wald, Robert M.

doi:10.1063/1.525365

Cited by 43 publications

(37 citation statements)

References 3 publications

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“…Physically, when (x 0 ) 2 g 00 → −∞, any certain observers, like a spaceship (corresponds to an arbitrary timelike curve), could not arrive at the singularity in the origin r = 0. We could prove that the integrated acceleration must satisfy [23][24][25]:…”

Section: Behavior Of Timelike Observer Under This Metricmentioning

confidence: 99%

Behavior of a vacuum and naked singularity under a smooth gauge function in Lyra geometry

Zhi

2018

Can. J. Phys.

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Lyra geometry is a conformal geometry originated from Weyl geometry. In this article, we derive the exterior field equation under spherically symmetric gauge function x 0 (r) and metric in Lyra geometry. When we impose a specific form of the gauge function x 0 (r), the radial differential equation of the metric component g 00 will possess an irregular singular point(ISP) at r = 0.Moreover, we apply the method of dominant balance and then get the asymptotic behavior of the new spacetime solution. The significance of this work is that we could use a series of smooth gauge functions x 0 (r) to modulate the degree of divergence of the singularity at r = 0 and the singularity will become a naked singularity under certain conditions. Furthermore, we investigate the physical meaning of this novel behavior of spacetime in Lyra geometry and find out that no spaceship with finite integrated acceleration could arrive at this singularity at r = 0. The physical meaning of gauge function and integrability is also discussed.

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Section: Behavior Of Timelike Observer Under This Metricmentioning

confidence: 99%

Behavior of a vacuum and naked singularity under a smooth gauge function in Lyra geometry

Zhi

2018

Can. J. Phys.

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“…There are several other different ways of constructing a boundary (not necessarily 'causal') for Lorentzian manifolds (see [11,36,3,26,37]). Almost all of them have failed to give a boundary with adequate topological properties for some examples [13,24,16]. This has led some researchers to the opinion that not every distinguishing spacetime possesses a proper boundary.…”

Section: Causal Extensions Causal Diagrams and Causal Boundary Of Spmentioning

confidence: 99%

Vladimir Maksimovich Tuchkevich (on his eightieth birthday)

Aleksandrov¹,

Алферов²,

Basov³

et al. 1984

Sov. Phys. Usp.

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We define and study a new kind of relation between two diffeomorphic Lorentzian manifolds called a causal relation, which is any diffeomorphism characterized by mapping every causal vector of the first manifold onto a causal vector of the second. We perform a thorough study of the mathematical properties of causal relations and prove in particular that two given Lorentzian manifolds (say V and W ) may be causally related only in one direction (say from V to W , but not from W to V ). This leads us to the concept of causally equivalent (or isocausal in short) Lorentzian manifolds as those mutually causally related and to a definition of causal structure over a differentiable manifold as the equivalence class formed by isocausal Lorentzian metrics upon it.Isocausality is a more general concept than the conformal relationship, because we prove the remarkable result that a conformal relation ϕ is characterized by the fact of being a causal relation of the particular kind in which both ϕ and ϕ −1 are causal relations. Isocausal Lorentzian manifolds are mutually causally compatible, they share some important causal properties, and there are one-to-one correspondences, which are sometimes non-trivial, between several classes of their respective future (and past) objects. A more important feature is that they satisfy the same standard causality constraints. We also introduce a partial order for the equivalence classes of isocausal Lorentzian manifolds providing a classification of all the causal structures that a given fixed manifold can have.By introducing the concept of causal extension we put forward a new definition of causal boundary for Lorentzian manifolds based on the concept of isocausality, and thereby we generalize the traditional Penrose constructions of conformal infinity, diagrams and embeddings. In particular, the concept of causal diagram is given.Many explicit clarifying examples are presented throughout the paper.

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“…Some efforts are made to define a singular boundary which is coordinate independent, such as the "g-boundary" [3] and the "b-boundary" [4]. These prescriptions and other similar procedures, however, produce pathological topological boundaries in simple examples [1,5,6]. Hence, the singular boundary cannot be generally defined.…”

Section: Introductionmentioning

confidence: 99%

A $$1+5$$ 1 + 5 -dimensional gravitational-wave solution: curvature singularity and spacetime singularity

Chen

Dai

2017

Eur. Phys. J. C

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We solve a 1 + 5-dimensional cylindrical gravitational-wave solution of the Einstein equation, in which there are two curvature singularities. Then we show that one of the curvature singularities can be removed by an extension of the spacetime. The result exemplifies that the curvature singularity is not always a spacetime singularity; in other words, the curvature singularity cannot serve as a criterion for spacetime singularities.

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Singular boundaries of space–times

Cited by 43 publications

References 3 publications

Behavior of a vacuum and naked singularity under a smooth gauge function in Lyra geometry

Behavior of a vacuum and naked singularity under a smooth gauge function in Lyra geometry

Vladimir Maksimovich Tuchkevich (on his eightieth birthday)

A $$1+5$$ 1 + 5 -dimensional gravitational-wave solution: curvature singularity and spacetime singularity

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