Chronological Spacetimes without Lightlike Lines are Stably Causal

Minguzzi, E.

doi:10.1007/s00220-009-0784-6

Cited by 34 publications

(60 citation statements)

References 31 publications

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“…Such conditions have been considered in [18], [14], [5]. An explicit example, which here we express in the future direction, is the following; see Prop.…”

Section: Context and Theoremmentioning

confidence: 99%

Cosmological singularities from high matter density without global topological assumptions

Lesourd

2019

Gen Relativ Gravit

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Cosmological singularity theorems such as that of Hawking and Penrose assume local curvature conditions as well as global ones like the existence of a compact (achronal) slice. Here, we prove a new singularity theorem for chronological spacetimes that satisfy what we call a 'past null focusing' condition. Such a condition forces all null geodesics γ : [0, a) → M with future endpoint γ(0) to develop a pair of conjugate points if past complete. By the Einstein field equations, such a condition will be satisfied if the density of matter fields remains sufficiently high towards the past of the spacetime, as may be expected in certain cosmological scenarios. The theorem obtained doesn't make starting assumptions about the spacetime's topology, such as the existence of a compact achronal slice, and if in addition to a 'past null focusing' condition we assume the timelike convergence condition, then further consequences pertaining to the existence of CMC foliations and the character of the singularity are obtained. With the addition of the timelike convergence condition, we obtain the conclusion that all timelike geodesics are past incomplete, rather than the existence of a single incomplete non-spacelike geodesic.

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“…Such conditions have been considered in [18], [14], [5]. An explicit example, which here we express in the future direction, is the following; see Prop.…”

Section: Context and Theoremmentioning

confidence: 99%

Cosmological singularities from high matter density without global topological assumptions

Lesourd

2019

Gen Relativ Gravit

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“…I proved [21,22] Theorem (Time begins just outside the chronology violating set at the beginning of the universe). Let (M, g) be a spacetime which is either chronological or admits a chronology violating class which generates the whole universe, i.e.…”

Section: A Theorem On the Origin Of Timementioning

confidence: 99%

Chronology violations and the origin of time

Minguzzi

2013

EPJ Web of Conferences

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Abstract. We review some results which relate chronology violations to singularities, and explain how the absence of both pathologies implies the existence of a cosmological time. Building on these mathematical ideas we then propose a causality argument in order to solve the homogeneity and entropy problems of cosmology. The solution is based on the replacement of the spacelike Big Bang boundary with a null boundary behind which stays a chronology violating region. This solution requiring a tilting of the light cones near the null boundary is based more on the behavior of the light cones and hence on causality, than on the behavior of the scale factor (expansion). The philosophical connection of this picture with Augustine of Hyppo famous discussion on time and creation is commented.

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“…For more details we refer the reader to [8], [10,11] and [30,31]. Definition : K + is the smallest relation containing I + that is topologically closed and transitive.…”

Section: Causal Structure Of Space-timescausality Conditions and Caumentioning

confidence: 99%

Causal cones, cone preserving transformations and causal structure in special and general relativity

Janardhan¹,

Saraykar

2013

Gravit. Cosmol.

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We present a short review of geometric and algebraic approach to causal cones and describe cone preserving transformations and their relationship with causal structure related to special and general theory of relativity. We describe Lie groups, especially matrix Lie groups, homogeneous and symmetric spaces and causal cones and certain implications of these concepts in special and general theory of relativity related to causal structure and topology of space-time. We compare and contrast the results on causal relations with those in the literature for general spacetimes and compare these relations with K-causal maps. We also describe causal orientations and their implications for space-time topology and discuss some more topologies on space-time which arise as an application of domain theory. PACS numbers: 02.40 Sf , 04.20 Gz.

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Chronological Spacetimes without Lightlike Lines are Stably Causal

Cited by 34 publications

References 31 publications

Cosmological singularities from high matter density without global topological assumptions

Cosmological singularities from high matter density without global topological assumptions

Chronology violations and the origin of time

Causal cones, cone preserving transformations and causal structure in special and general relativity

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