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

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

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 $\Lambda$-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

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 Λ\LambdaCDM

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 $\Lambda$-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