Energy conditions and spacetime singularities

Tipler, Frank J.

doi:10.1103/physrevd.17.2521

Cited by 199 publications

(176 citation statements)

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“…Concerning the energy assum ption, which is SEC plus generic condition in order to assure the exist ence of conjugat e point s, some results were found in [218], lat er corrected in [39], by using the averaged condit ions referred to in subsect ion 2.1 just before P roposit ion 2.4. T hese results were lat er improved in [27,118].…”

Section: T H E or E M 5 6 ( H Aw Kin G An D P E N R O S E )mentioning

confidence: 99%

“…Obviously, t he Raychaudhuri equat ion (27) has a term proport ional to the Ricci tensor, which may be discont inuous. In general this will not modify the result s of P roposit ions 2.3, 2.4, 2.7 and 2.8, but it will change the improved results mentioned several times in which the geodesic focusing takes place assuming only an averaged SEC or similar, as they usually assum e t he continuity of the term involving the Ricci tensor [27,28,218]. C u r v at u r e g r ow t h .…”

Section: N O R M Al N E Ig H B O U R H O O D S An D C O or D In A T Ementioning

confidence: 99%

“…However, this condit ion can be relaxed subst ant ially but still maint aining the focusing eOE ect of P roposit ion 2.3 (see Refs. 27,218,165) . T he required assumptions are usually of int egral typ e, so that t he quant ity R m u u m u u is required to be non-negat ive in an adequat e averaged sense [27,28,218].…”

Section: P R O P O S It Io N 2 3 If the Expansion Of The F-d T Imementioning

confidence: 99%

“…27,218,165) . T he required assumptions are usually of int egral typ e, so that t he quant ity R m u u m u u is required to be non-negat ive in an adequat e averaged sense [27,28,218]. P roposit ion 2.3 can be also generalized in a more relevant manner by the following st andard result [12,27,72,107].…”

Section: P R O P O S It Io N 2 3 If the Expansion Of The F-d T Imementioning

confidence: 99%

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Singularity Theorems and Their Consequences

Senovilla¹

1998

General Relativity and Gravitation

252

378

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Rece ived Septem be r 2 4, 1 997. Rev . ve rsion Febr u ar y 26 , 19 98A detailed study of the singu larity t heorem s is present ed . I discuss the plausibility and reason ability of t heir hy pot heses, t he ap plicability an d im plicat ions of t he theorem s, as well as the t heorem s t hem selves. T he consequences usually ex t ract ed from t hem , som e of t hem w it hout the necessa ry rigour, are widely and carefu lly an aly sed w it h m any clarify ing ex am ples an d alternat ive view s.

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Section: T H E or E M 5 6 ( H Aw Kin G An D P E N R O S E )mentioning

confidence: 99%

Section: N O R M Al N E Ig H B O U R H O O D S An D C O or D In A T Ementioning

confidence: 99%

Section: P R O P O S It Io N 2 3 If the Expansion Of The F-d T Imementioning

confidence: 99%

Section: P R O P O S It Io N 2 3 If the Expansion Of The F-d T Imementioning

confidence: 99%

See 2 more Smart Citations

Singularity Theorems and Their Consequences

Senovilla¹

1998

General Relativity and Gravitation

252

378

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“…In the context of string cosmology, it is important to note that a pre-big-bang phase must necessarily be born out of matter violating the WEC. lt would be instructive to check out the averaged energy conditions (AWEC, ANEC) [25] for this phase. Matter fields which generate a pre-big-bang phase could therefore be quantum in nature, considering the fact that quantum stress tensors can in principle violate the local energy conditions [26] but may satisfy their global (averaged) versions.…”

Section: Frw-like Eramentioning

confidence: 99%

Scale factor duality and the energy condition inequalities

Kar

1997

Physics Letters B

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We demonstrate, by a simple analysis, that cosmological line elements related by scale factor duality also exhibit a duality with respect to the conserva- Stringy cosmologies (for reviews, see [8], [9] ) have certain characteristic features apart from the symmetry of scale factor duality. Firstly, one does not need to bring in an ad-hoc scalar field to get the necessary inflationary phase. The dilaton field which arises as one of the massless excitations of the string world sheet serves the purpose. Moreover, there exists the notion of a phase termed as pre-big-bang (t < 0) during which we have a rapidly inflating universe with a scale factor generically obeying a pole law ( a(t) = (−t) β ; (β < 0 ). This new phase is expected to end at t = 0 where a FRW evolution (a(t) = t β ; 0 < β < 1) takes over and we finally end up with our universe today. Unfortunately, the transition from the pre-big-bang epoch to the FRW phase is plagued by the presence of a singularity, which, if absent would have solved the problem of singularities in GR, at least, in a cosmological setting. The generic presence of a singularity in the transition epoch which spoils a smooth crossover has been termed as the graceful exit problem in string cosmology [10]. Recently, Rey [11] has claimed that by introducing quantum back reaction it is possible to avoid the graceful exit problem at least within the limits of a two dimensional model like that of CGHS [12]. Whether an extension of this to four dimensions is possible or not is still an open question. On the other hand, a quantum cosmology approach to graceful exit has been advocated in [13]. The low energy effective theory that emerges out of string theory is much like Einstein gravity. The equations are derivable from an action which resembles that of a Brans-Dicke 2 theory with the ω parameter set to −1. Specifically, one has :This is the bosonic sector of the genus-zero, low energy action for closed superstrings in the limit when inverse string tension (or α ′ ) goes to zero. Here, H µνλ is the third-rank antisymmetric tensor field, φ the dilaton field and V contains contributions from the dilaton potential and the cosmological constant. The β function equations which are obtained by imposing quantum conformal invariance in the worldsheet sigma model can be derived from this action by performing appropriate variations.Obviously, there are two frames in which the metrics look very different-the string (Brans-Dicke) and the Einstein frame. These frames are related to each other by a conformal transformation. We shall exclusively work in the string frame.The Einstein-like equations can be written in the form G µν = e 2φ T µν where T µν = T φ µν + T M µν (M denotes matter fields other than the dilaton). These equations are exactly those for Brans-Dicke theory with the parameter ω = −1. One might argue that it is not proper to rewrite the β function equations in an explicit Einstein form because at the level of the worldsheet sigma model g µν , φ or B µν -all have the same status-they ...

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Topological censorship and chronology protection

Friedman¹,

Higuchi²

2006

Ann. Phys.

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Over the past two decades, substantial efforts have been made to understand the way in which physics enforces the ordinary topology and causal structure that we observe, from subnuclear to cosmological scales. We review the status of topological censorship and the topology of event horizons; chronology protection in classical and semiclassical gravity; and related progress in establishing quantum energy inequalities.Comment: Dedicated to Rafael Sorkin, whose tutoring and friendship from third grade on is responsible for one of us (JF) having spent his adult life in physics and whose work has inspired both of us. In v.2, some references are updated, and references are added to early work on 2+1 spacetimes and to work on event-horizon topolog

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Energy conditions and spacetime singularities

Cited by 199 publications

References 12 publications

Singularity Theorems and Their Consequences

Singularity Theorems and Their Consequences

Scale factor duality and the energy condition inequalities

Topological censorship and chronology protection

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