120 research outputs found
Lanczos potentials and a definition of gravitational entropy for perturbed FLRW space-times
We give a prescription for constructing a Lanczos potential for a
cosmological model which is a purely gravitational perturbation of a
Friedman-Lemaitre-Robertson-Walker space-time. For the radiation equation of
state, we find the Lanczos potential explicitly via Fourier transforms. As an
application, we follow up a suggestion of Penrose and propose a definition of
gravitational entropy for these cosmologies. With this definition, the
gravitational entropy initially is finite if and only if the initial Weyl
tensor is finite.Comment: 16 pages, submitted for publication in Classical and Quantum Gravit
Formation of Higher-dimensional Topological Black Holes
We study higher dimensional gravitational collapse to topological black holes
in two steps. Firstly, we construct some (n+2)-dimensional collapsing
space-times, which include generalised Lemaitre-Tolman-Bondi-like solutions,
and we prove that these can be matched to static -vacuum exterior
space-times. We then investigate the global properties of the matched solutions
which, besides black holes, may include the existence of naked singularities
and wormholes. Secondly, we consider as interiors classes of 5-dimensional
collapsing solutions built on Riemannian Bianchi IX spatial metrics matched to
radiating exteriors given by the Bizon-Chmaj-Schmidt metric. In some cases, the
data at the boundary for the exterior can be chosen to be close to the data for
the Schwarzschild solution.Comment: 16 pages, 3 figures; v2: typos corrected, matches final published
versio
Avoiding closed timelike curves with a collapsing rotating null dust shell
We present an idealised model of gravitational collapse, describing a
collapsing rotating cylindrical shell of null dust in flat space, with the
metric of a spinning cosmic string as the exterior. We find that the shell
bounces before closed timelike curves can be formed. Our results also suggest
slightly different definitions for the mass and angular momentum of the string.Comment: 6 pages; v2: references added; v3: remark added for final published
versio
Spherically symmetric models: separating expansion from contraction in models with anisotropic pressures
We investigate spherically symmetric spacetimes with an anisotropic fluid and
discuss the existence and stability of a dividing shell separating expanding
and collapsing regions. We find that the dividing shell is defined by a
relation between the pressure gradients, both isotropic and anisotropic, and
the strength of the fields induced by the Misner-Sharpe mass inside the
separating shell and by the pressure fluxes. This balance is a generalization
of the Tolman-Oppenheimer- Volkoff equilibrium condition which defines a local
equilibrium condition, but conveys also a non- local character given the
definition of the Misner-Sharpe mass. We present a particular solution with
dust and radiation that provides an illustration of our results.Comment: 4pp Towards New Paradigms: Proceeding Of The Spanish Relativity
Meeting 2011. AIP Conference Proceedings, Volume 1458, pp. 487-490 (2012).
Published in AIP Conf.Proc. 1458 (2011) 487-49
Separating expansion from contraction: generalized TOV condition, LTB models with pressure and CDM
We discuss the existence of a dividing shell separating expanding and
collapsing regions in spherically symmetric solutions with pressure. We obtain
gauge invariant conditions relating not only the intrinsic spatial curvature of
the shells to the ADM mass, but also a function of the pressure which we
introduce that generalises the Tolman-Oppenheimer-Volkoff equilibrium
condition, in the framework of a 3+1 spacetime splitting. We consider the
particular case of a Lema\^itre-Tolman-Bondi dust models with a cosmological
constant (a -CDM model) as an example of our results.Comment: Proceedings of 'Invisible Universe International Conference', Paris,
June 29- July 3, 2009 ; 5pp, 4 fig
The Einstein-Friedrich-nonlinear scalar field system and the stability of scalar field Cosmologies
A frame representation is used to derive a first order quasi-linear symmetric
hyperbolic system for a scalar field minimally coupled to gravity. This
procedure is inspired by similar evolution equations introduced by Friedrich to
study the Einstein-Euler system. The resulting evolution system is used to show
that small nonlinear perturbations of expanding
Friedman-Lema\^itre-Robertson-Walker backgrounds, with scalar field potentials
satisfying certain future asymptotic conditions, decay exponentially to zero,
in synchronous time.Comment: Version 4: Matches final published versio
Lanczos potentials for linearly perturbed FLRW spacetimes
We study the problem of deriving the Lanczos potential and superpotential for linearly perturbed Friedman-Lemaitre-Robertson-Walker (FLRW) spacetimes.FCM thanks FCT (Portugal) for grant SFRH/BPD/12137/2003 and Centre of Mathematics(CMAT), University of Minho, for support
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