Geodesic completeness of orthogonally transitive cylindrical space–times

Fernández–Jambrina, L.

doi:10.1063/1.532940

Cited by 7 publications

(8 citation statements)

References 15 publications

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“…Nevertheless, in an e-mail dated on September the 9th, 1998, he mentioned that a letter proving the vanishing of spatial averages "following his earlier method" had already been submitted for publication. This private announcement was followed, shortly thereafter, by (i) another paper by Dadhich and AKR [8] where they proved the existence of oscillatory non-singular models within the non-perfect fluid spherically symmetric family of [4] mentioned above, (ii) general theorems providing sufficient conditions for the geodesic completeness of general cylindrically symmetric spacetimes [15,12] and (iii) some work [19] showing the relevance that the singularity-free solutions might have in the fashionable String Cosmology, see also [18] and references therein.…”

Section: History Of the Conjecturementioning

confidence: 99%

A singularity theorem based on spatial averages

Senovilla

2007

Pramana - J Phys

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Abstract. Inspired by Raychaudhuri's work, and using the equation named after him as a basic ingredient, a new singularity theorem is proved. Open non-rotating everywhere expanding universes with non-vanishing spatial average of the matter variables are severely geodesically incomplete to the past. Another way of stating the result is that, under the same conditions, any singularity-free model must have a vanishing spatial average of the energy density (and other physical variables). This is very satisfactory and provides a clear decisive difference between singular and non-singular cosmologies.

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Section: History Of the Conjecturementioning

confidence: 99%

A singularity theorem based on spatial averages

Senovilla

2007

Pramana - J Phys

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“…6 Another estrategy to approach singularities arose with the publication of regularity theorems. [7][8][9] Whereas singularity theorems stated general sufficient conditions for the appearance of singularities, these theorems aimed the contrary, namely particular conditions to achieve regular space-times.…”

Section: Introductionmentioning

confidence: 99%

Nonsingular G2 stiff fluid cosmologies

Fernández–Jambrina

González-Romero

2004

Journal of Mathematical Physics

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Gravitational waves in vacuum spacetimes with cosmological constant. I. Classification and geometrical properties of nontwisting type N solutions J. Math. Phys. 40, 4495 (1999) In this paper we analyze Abelian diagonal orthogonally transitive space-times with spacelike orbits for which the matter content is a stiff perfect fluid. The Einstein equations are cast in a suitable form for determining their geodesic completeness. A sufficient condition on the metric of these space-times is obtained, that is fairly easy to check and to implement in exact solutions. These results confirm that nonsingular space-times are abundant among stiff fluid cosmologies.

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“…Therefore, it is convenient to have a general result that may simplify the task of analyzing the issue of geodesic completeness. This matter is addressed for the diagonal case in [14,13] and for the nondiagonal case in [12]. It has been proved that, a cylindrically symmetric diagonal metric of the form [14,Sec.…”

Section: Definition 416mentioning

confidence: 99%

“…such that the axis located at r = 0 has been proved in [12] that it has complete future geodesics if a set of conditions (see [12, conditions (1)-(4)]) is fulfilled. Just changing the sign of the time derivatives in the previous one, a theorem can be obtained for past-pointing geodesics.…”

Section: Definition 416mentioning

confidence: 99%