Line integration of Ricci curvature and conjugate points in Lorentzian and Riemannian manifolds

Chicone, Carmen; Ehrlich, Paul E.

doi:10.1007/bf01303279

Cited by 41 publications

(38 citation statements)

References 19 publications

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“…It follows from the existence of some pair of conjugate points in the lightlike geodesics accordingly to [11,Prop. 4 This proposition has been improved by Tipler [30,31] and Chicone and Ehrlich [6] (see also Borde [5]) by weakening the null convergence condition to the averaged null convergence condition. This possibility is important because many quantum fields on spacetime determine a stress-energy tensor and hence a Ricci tensor which does not comply with the null convergence condition while it satisfies the averaged null convergence condition.…”

Section: Absence Of Lightlike Linesmentioning

confidence: 99%

Chronological Spacetimes without Lightlike Lines are Stably Causal

Minguzzi

2009

Commun. Math. Phys.

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The statement of the title is proved. It implies that under physically reasonable conditions, spacetimes which are free from singularities are necessarily stably causal and hence admit a time function. Read as a singularity theorem it states that if there is some form of causality violation on spacetime then either it is the worst possible, namely violation of chronology, or there is a singularity. The analogous result: "Non-totally vicious spacetimes without lightlike rays are globally hyperbolic" is also proved, and its physical consequences are explored.

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Section: Absence Of Lightlike Linesmentioning

confidence: 99%

Chronological Spacetimes without Lightlike Lines are Stably Causal

Minguzzi

2009

Commun. Math. Phys.

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“…where the average is taken over a null geodesic, K µ is the affinely parameterized tangent to the geodesic, and λ is an affine parameter [4,5,6,7,8,9,10,11,12,13,14].…”

Section: Energy Conditionsmentioning

confidence: 99%

Some Thoughts on Energy Conditions and Wormholes

Roman

2006

The Tenth Marcel Grossmann Meeting

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This essay reviews some of the recent progress in the area of energy conditions and wormholes. Most of the discussion centers on the subject of "quantum inequality" restrictions on negative energy. These are bounds on the magnitude and duration of negative energy which put rather severe constraints on its possible macroscopic effects. Such effects might include the construction of wormholes and warp drives for faster-than-light travel, and violations of the second law of thermodynamics. Open problems and future directions are also discussed. *

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“…It is known from some of this work [30,31,27] that what is important in order to ensure focusing is that R ab U a U b (where U a is the tangent to a null or a timelike geodesic) obey an integral inequality, not necessarily one that must hold at each point. Such integral -or, as they have come to be called, averaged -convergence conditions will do just as well for the purposes of this paper.…”

Section: Appendix A: Convergence Conditions and Energymentioning

confidence: 99%

Open and closed universes, initial singularities, and inflation

1994

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The existence of initial singularities in expanding universes is proved without assuming the timelike convergence condition. The assumptions made in the proof are ones likely to hold both in open universes and in many closed ones. (It is further argued that at least some of the expanding closed universes that do not obey a key assumption of the theorem will have initial singularities on other grounds.) The result is significant for two reasons: (a) previous closed-universe singularity theorems have assumed the timelike convergence condition, and (b) the timelike convergence condition is known to be violated in inflationary spacetimes. An immediate consequence of this theorem is that a recent result on initial singularities in open, future-eternal, inflating spacetimes may now be extended to include many closed universes. Also, as a fringe benefit, the time-reverse of the theorem may be applied to gravitational collapse.

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Line integration of Ricci curvature and conjugate points in Lorentzian and Riemannian manifolds

Cited by 41 publications

References 19 publications

Chronological Spacetimes without Lightlike Lines are Stably Causal

Chronological Spacetimes without Lightlike Lines are Stably Causal

Some Thoughts on Energy Conditions and Wormholes

Open and closed universes, initial singularities, and inflation

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