127 research outputs found
Singularities of varying light speed cosmologies
We study the possible singularities of isotropic cosmological models that
have a varying speed of light as well as a varying gravitational constant. The
field equations typically reduce to two dimensional systems which are then
analyzed both by dynamical systems techniques in phase space and by applying
the method of asymptotic splittings. In the general case we find initially
expanding closed models which recollapse to a future singularity and open
universes that are eternally expanding towards the future. The precise nature
of the singularities is also discussed.Comment: 7 pages, 2 figures, uses iop style files, to appear in the
Proceedings of the Greek Relativity Meeting NEB12, June 29-July 2, 2006,
Nauplia, Greec
Slice Energy and Theories of Gravitation
We review recent work on the use of the slice energy concept in generalized
theories of gravitation. We focus on two special features in these theories,
namely, the energy exchange between the matter component and the scalar field
generated by the conformal transformation to the Einstein frame of such
theories and the issue of the physical equivalence of different conformal frame
representations. We show that all such conformally-related, generalized
theories of gravitation allow for the slice energy to be invariably defined and
its fundamental properties be insensitive to conformal transformations.Comment: 16 pages, In: Proceedings of the 11th Greek Relativity Meetin
Slice Energy in Higher Order Gravity Theories and Conformal Transformations
We study the generic transport of slice energy between the scalar field
generated by the conformal transformation of higher-order gravity theories and
the matter component. We give precise relations for this exchange in the cases
of dust and perfect fluids. We show that, unless we are in a stationary
spacetime where slice energy is always conserved, in non-stationary situations
contributions to the total slice energy depend on whether or not test matter
follows geodesics in both frame representations of the dynamics, that is on
whether or not the two conformally related frames are physically
indistinguishable.Comment: 18 pages, references added, remark added in last Section related to
the choice of physical frame, various other improvements, final version to
appear in Gravitation and Cosmolog
Geodesics at Sudden Singularities
We show that a general solution of the Einstein equations that describes
approach to an inhomogeneous and anisotropic sudden spacetime singularity does
not experience geodesic incompleteness. This generalises the result established
for isotropic and homogeneous universes. Further discussion of the weakness of
the singularity is also included.Comment: v2: 7 pages, minor improvements, version to appear in PR
Brane singularities and their avoidance
The singularity structure and the corresponding asymptotic behavior of a
3-brane coupled to a scalar field or to a perfect fluid in a five-dimensional
bulk is analyzed in full generality using the method of asymptotic splittings.
In the case of the scalar field, it is shown that the collapse singularity at a
finite distance from the brane can be avoided only at the expense of making the
brane world-volume positively or negatively curved. In the case where the bulk
field content is parametrized by an analogue of perfect fluid with an arbitrary
equation of state P=\gamma\rho between the `pressure' P and the `density' \rho,
our results depend crucially on the constant fluid parameter \gamma: (i) For
\gamma>-1/2, the flat brane solution suffers from a collapse singularity at
finite distance, that disappears in the curved case. (ii) For \gamma<-1, the
singularity cannot be avoided and it becomes of the big rip type for a flat
brane. (iii) For -1<\gamma< or = -1/2, the surprising result is found that
while the curved brane solution is singular, the flat brane is not, opening the
possibility for a revival of the self-tuning proposal.Comment: 37 pages, latex, merged version of arXiv:1005.3221 and
arXiv:1004.3379, to appear in Class.Quant.Gra
Variational and conformal structure of nonlinear metric-connection gravitational lagrangians
We examine the variational and conformal structures of higher order theories
of gravity which are derived from a metric-connection Lagrangian that is an
arbitrary function of the curvature invariants. We show that the constrained
first order formalism when applied to these theories may lead consistently to a
new method of reduction of order of the associated field equations. We show
that the similarity of the field equations which are derived from appropriate
actions via this formalism to those produced by Hilbert varying purely metric
Lagrangians is not merely formal but is implied by the diffeomorphism covariant
property of the associated Lagrangians. We prove that the conformal equivalence
theorem of these theories with general relativity plus a scalar field, holds in
the extended framework of Weyl geometry with the same forms of field and
self-interacting potential but, in addition, there is a new `source term' which
plays the role of a stress. We point out how these results may be further
exploited and address a number of new issues that arise from this analysis.Comment: 8 pages, LaTeX (REVTeX 3.1), submitted to J. Math. Phys., references
added (nothing changed but LaTeX style
Series expansions and sudden singularities
We construct solutions of the Friedmann equations near a sudden singularity
using generalized series expansions for the scale factor, the density, and the
pressure of the fluid content. In this way, we are able to arrive at a solution
with a sudden singularity containing two free constants, as required for a
general solution of the cosmological equations.Comment: 4 pages, contribution for the Proceedings of the MG13 Meeting on
General Relativity, Stockholm, July 201
Comment to the paper `Conformal transformations single out a unique measure of distance'
We discuss the consequences of the incorrectness [see the Erratum in Phys.
Rev D 49, 1145 (1994)] of that paper and add two related remarks. The scope of
this comment is to encourage further research on: `Which of the conformally
equivalent metrics is the physical one?'Comment: 4 pages, LaTeX, published in Phys. Rev. D52, 6198 (1995
- …