Probing the creatable character of perturbed Friedmann-Robertson-Walker universes

2011

Gen Relativ Gravit

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We present a new approach to the question of properly defining energy and momenta for non asymptotically Minkowskian spaces in general relativity, in the case where these energy and momenta are conserved. In order to do this, we first prove that there always exist some special Gauss coordinates for which the conserved linear and angular three-momenta vanish. This allows us to consider the case of creatable universes (the universes whose proper 4-momenta vanish) in a consistent way, which is the main interest of the paper. When applied to the Friedmann-Lema{\^{\i}}tre-Robertson-Walker case, perturbed or not, our formalism leads to previous results, according to most literature on the subject. Some future work that should be done is mentioned.Comment: Enlarged and modified version, where several comments have been added (20 pages), of the previous manuscript: "Creatable universes: a new, and more consistent and general approach". In particular, changes involve a new title and updated references. Accepted in General Relativity and Gravitatio

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“…On the other hand, it can be easily seen that in the present new approach, as in [25], perturbed closed FLRW universes are creatable, while perturbed open FLRW universes are not.…”

Section: The Perturbed Flrw Universesmentioning

confidence: 83%

“…[25]) that P 0 = +∞. Then, we can assert that our perturbed flat FLRW universe is really a non creatable one.…”

Section: The Perturbed Flrw Universesmentioning

confidence: 89%

Section: The Perturbed Flrw Universesmentioning

confidence: 92%

“…(25) and (26) (the first one up to zero order in t − t 0 and order one in x 3 ). On the other hand, the time derivatives ∂ 0 g 3i , ∂ 0 g aa , must…”

Section: Appendix B: Fitting Conveniently the Functions λ And θ Or Thmentioning

confidence: 99%

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Intrinsic vanishing of energy and momenta in a universe

2011

Gen Relativ Gravit

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“…According to this criterion it could only be represented by a creatable universe. Thus, in [6], it was proved that, within the inflationary perturbed Friedmann-Lemaître-Robertson-Walker universes, only the closed case corresponds to a creatable universe.…”

Section: Final Considerationsmentioning

confidence: 99%

Creatable universes: A new approach

2010

J. Phys.: Conf. Ser.

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Abstract. We are interested in the non asymptotically flat space-times for which all the momenta (energy, 3-momentum and angular 4-momenta) are conserved in time. We call universes such space-times. Starting from the Weinberg definition of the momenta associated to a spacelike 3-surface, we give a coordinate prescription to properly define the energy of a universe. The prescription includes the vanishing of linear and angular 3-momenta. This result allows us to consider the case of universes with vanishing 4-momenta (creatable universes) in a consistent way. IntroductionPeople have speculated about the possibility that our Universe came out from a vacuum quantum fluctuation [1,2]. In this case, one could expect that the resulting universe had vanishing energy, P 0 , and ever better, vanishing energy-momentum, P α , and vanishing angular 4-momentum J αβ .But the problem is the dramatic dependence of these momenta on the coordinate system used, letting aside the particular case of asymptotically flat space-times where one knows how to choose the good coordinate systems, as it is well known [3,4]. Nevertheless, if we want to deal with a space-time, V 4 , which could represent our Universe, we cannot always impose this asymptotic flatness.To circumvent this problem of lack of uniqueness in the definition of these momenta, in [5] we explain why we think that we must deal with Gauss coordinates in V 4 , based on some space-like 3-surface Σ 3 . Even more, we discussed why we should take coordinates which, at the same time, allow to write the corresponding instantaneous 3-space metric in a conformally flat way on the boundary, Σ 2 , of Σ 3 .But, this choice of coordinates let still a lot of freedom. Then, in the present paper, we impose further that our coordinates be such that the corresponding 3-momenta, P i and J ij , vanish. To do this, we previously prove that in any universe (i. e. a space-time where, once the convenient coordinate system has been choose, the defined 4-momenta remain constant in time) we always can change Σ 3 , without changing Σ 2 , such that P i = J ij = 0.Finally, in a general and consistent way, we can define a creatable universe as a universe where the 4-momenta, defined in the above coordinate systems, vanish. As we have just said, these are coordinate systems which are Gauss coordinate systems, where P i = J ij = 0, and where the instantaneous space metric can be written in a conformally flat way on Σ 2 . We will call these coordinate systems intrinsic coordinate systems.

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On the Uniqueness of the Energy and Momenta of an Asymptotically Minkowskian Space-Time: The Case of the Schwarzschild Metric

Springer Proceedings in Mathematics &Amp; Statistics

2013