A singularity theorem based on spatial averages

Senovilla, José M. M.

doi:10.1007/s12043-007-0109-2

“…Therefore, if such spatial averages do not vanish then the model must be singular. More details and a recent proof of the conjecture is available in the article by Senovilla in this volume [44]. Despite the conflict between whether spatial or spacetime averages was the crucial distinguishing factor between singular and non-singular models, it goes without saying that Raychaudhuri's idea about averages being a deciding factor will surely be remembered as a lasting contribution apart from his coveted equations.…”

Section: A Theorem For Non-rotating Singularity-free Universes: Raychmentioning

confidence: 99%

The Raychaudhuri equations: A brief review

Kar

¹

,

SenGupta

²

2007

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We present a brief review on the Raychaudhuri equations. Beginning with a summary of the essential features of the original article by Raychaudhuri and subsequent work of numerous authors, we move on to a discussion of the equations in the context of alternate non-Riemannian spacetimes as well as other theories of gravity, with a special mention on the equations in spacetimes with torsion (Einstein-Cartan-Sciama-Kibble theory). Finally, we give an overview of some recent applications of these equations in general relativity, quantum field theory, string theory and the theory of relativisitic membranes. We conclude with a summary and provide our own perspectives on directions of future research. The beginningsAbout half a century ago, general relativity (GR) was young (just forty years old!), and even the understanding of the simplest solution, the Schwarzschild, was incomplete. Cosmology was virtually in its infancy, despite the fact that the FriedmannLemaitre-Robertson-Walker (FLRW) solutions had been around for quite a while. The question about the then-known exact solutions of GR, which worried the serious relativist quite a bit, concerned their singular nature. Both the Schwarzschild and the cosmological solutions were singular. It is well-known that the creator of GR, Einstein himself, was quite worried about the appearance of singularities in his theory. Was there a way out? Was it correct to believe in a theory which had singular solutions? Were singularities inevitable in GR?It was during these days in the early 1950s, Raychaudhuri began examining some of these questions in GR. One of his early works during this era involved the construction of a non-static solution of the Einstein equations for a cluster of radially moving particles in an otherwise empty space [1]. A year before, he had also written an article related to condensations in an expanding Universe [2] 49

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“…Recently, Senovilla (1990) obtained a new class of exact solution of Einstein's equations without big bang singularity, representing a cylindrically symmetric, inhomogeneous cosmological model field with perfect fluid which is smooth and regular everywhere satisfying energy and causality conditions Senovilla (2007) pointed out that all non-singular models were cosmological in the sense that they could not describe a finite star surrounded by a surface of vanishing pressure. However, it can certainly happen that the energy density falls off too quickly at large distances (this certainly occurred in all known singularity free solution).…”

Section: Introductionmentioning

confidence: 99%

“…However, it can certainly happen that the energy density falls off too quickly at large distances (this certainly occurred in all known singularity free solution). In every singularity free non rotating expanding globally hyperbolic model satisfying the strong energy condition, spatial averages of the matter variables vanish (Senovilla 2007). Thus a clear, decisive, difference between singular and regular (globally hyperbolic) expanding cosmological models is that the latter must have vanishing spatial averages of the matter variables (Senovilla 1998).…”

Section: Introductionmentioning

confidence: 99%

A new class of relativistic perfect fluid cylinders with expansion proportional to shear scalar

Gupta

¹

,

Kumar

²

,

Pratibha

³

2011

Astrophys Space Sci

1

0

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show abstract

“…Recently, Senovilla (1990) obtained a new class of exact solution of Einstein's equations without big bang singularity, representing a cylindrically symmetric, inhomogeneous cosmological model field with perfect fluid which is smooth and regular everywhere satisfying energy and causality conditions Senovilla (2007) pointed out that all non-singular models were cosmological in the sense that they could not describe a finite star surrounded by a surface of vanishing pressure. However, it can certainly happen that the energy density falls off too quickly at large distances (this certainly occurred in all known singularity free solution).…”

Section: Introductionmentioning

confidence: 99%

“…However, it can certainly happen that the energy density falls off too quickly at large distances (this certainly occurred in all known singularity free solution). In every singularity free non rotating expanding globally hyperbolic model satisfying the strong energy condition, spatial averages of the matter variables vanish (Senovilla 2007). Thus a clear, decisive, difference between singular and regular (globally hyperbolic) expanding cosmological models is that the latter must have a vanishing spatial averages of the matter variables (Senovilla 1998).…”

Section: Introductionmentioning

confidence: 99%