Filipe C. Mena

Local conditions separating expansion from collapse in spherically symmetric models with anisotropic pressures

The authors wish to thank the anonymous referee for many enlightening comments and suggestions and Jose Fernando Pascual-Sanchez for helpful discussions. M. Le D. also wishes to thank Michele Fontanini, Daniel Guariento and Elcio Abdalla for helpful discussions. The work of M. Le D. has been supported by CSIC (JAEDoc072), CICYT (FPA2006-05807) in Spain and FAPESP (2011/24089-5) in Brazil. F.C.M. thanks CMAT, Univ. Minho, for support through FEDER Funds COMPETE and FCT Projects No. Est-C/MAT/UI0013/2011, No. PTDC/MAT/108921/2008 and No. CERN/FP/123609/2011. M. Le D. and J. P. M. acknowledge the CAAULs Project No. PEst-OE/FIS/UI2751/2011. J. P. M. also wishes to thank FCT for Grants No. CERN/FP/123615/2011 and No. CERN/FP/123618/2011.

Cosmic no-hair: nonlinear asymptotic stability of de Sitter universe

We study the asymptotic stability of de Sitter spacetime with respect to nonlinear perturbations, by considering second-order perturbations of a flat Friedmann–Lemaitre–Robertson–Walker universe with dust and a positive cosmological constant. Using the synchronous co-moving gauge we find that, as in the case of linear perturbations, the nonlinear perturbations also tend to constants, asymptotically in time. Analysing curvature and other spacetime invariants, we show, however, that these quantities asymptotically tend to their de Sitter values, thus demonstrating that the geometry is indeed locally asymptotically de Sitter, despite the fact that matter inhomogeneities tend to constants in time. Our results support the inflationary picture of frozen amplitude matter perturbations that are stretched outside the horizon, and demonstrate the validity of the cosmic no-hair conjecture in the nonlinear inhomogeneous settings considered here.

EVOLUTION OF THE DENSITY CONTRAST IN INHOMOGENEOUS DUST MODELS

With the help of families of density contrast indicators, we study the tendency of gravitational systems to become increasingly lumpy with time. Depending upon their domain of definition, these indicators could be local or global. We make a comparative study of these indicators in the context of inhomogeneous cosmological models of Lemaitre-Tolman and Szekeres. In particular, we look at the temporal asymptotic behaviour of these indicators and ask under what conditions, and for which class of models, they evolve monotonically in time. We find that for the case of ever-expanding models, there is a larger class of indicators that grow monotonically with time, whereas the corresponding class for the recollapsing models is more restricted. Nevertheless, in the absence of decaying modes, indicators exist which grow monotonically with time for both ever-expanding and recollapsing models simultaneously. On the other hand, no such indicators may be found which grow monotonically if the decaying modes are allowed to exist. We also find the conditions for these indicators to be non-divergent at the initial singularity in both models. Our results can be of potential relevance for understanding structure formation in inhomogeneous settings and in debates regarding gravitational entropy and the arrow of time. In particular, the spatial dependence of turning points in inhomogeneous cosmologies may result in multiple density contrast arrows in recollapsing models over certain epochs. We also find that different notions of asymptotic homogenization may be deduced, depending upon the density contrast indicators used.

Separating expansion from contraction in spherically symmetric models with a perfect fluid: Generalization of the Tolman-Oppenheimer-Volkoff condition and application to models with a cosmological constant

We investigate spherically symmetric perfect-fluid spacetimes and discuss the existence and stability of a dividing shell separating expanding and collapsing regions. We perform a 3+1 splitting and obtain gauge invariant conditions relating the intrinsic spatial curvature of the shells to the Misner-Sharp mass and to a function of the pressure that we introduce and that generalizes the Tolman-Oppenheimer-Volkoff equilibrium condition. We find that surfaces fulfilling those two conditions fit, locally, the requirements of a dividing shell, and we argue that cosmological initial conditions should allow its global validity. We analyze the particular cases of the Lemaitre-Tolman-Bondi dust models with a cosmological constant as an example of a cold dark matter model with a cosmological constant ({Lambda}-CDM model) and its generalization to contain a central perfect-fluid core. These models provide simple but physically interesting illustrations of our results.

Separating expansion and collapse in general fluid models with heat flux

The work of M. Le D. has been supported by CSIC (JAEDoc072), CICYT (FPA2006-05807) in Spain and FAPESP (2011/24089-5) in Brazil. F. C. M. thanks CMAT, Universidade Minho, for support through FEDER Funds COMPETE, FCT Projects No. Est-C/MAT/UI0013/2011, No. PTDC/MAT/108921/2008, No. CERN/FP/123609/2011, and also Instituto de Fisica, UERJ, Rio de Janeiro, for hospitality. M. LeD. and J. P. M. acknowledge the CAAULs Project No. PEst-OE/FIS/UI2751/2011. J. P. M. also wishes to thank FCT for Grants No. CERN/FP/123615/2011 and No. CERN/FP/123618/2011. M. F. is supported by FAPESP Grant No. 2011/11365-4, D. C. G. is supported by FAPESP Grant No. 2010/08267-8, and E. A. is supported by FAPESP and CNPq.

Non-radial null geodesics in spherical dust collapse

The issue of the local visibility of the shell-focusing singularity in marginally bound spherical dust collapse is considered from the point of view of the existence of future-directed null geodesics with angular momentum which emanate from the singularity. The initial data (i.e. the initial density profile) at the onset of collapse is taken to be of class C 3 . Simple necessary and sufficient conditions for the existence of a naked singularity are derived in terms of the data. It is shown that there exist future-directed non-radial null geodesics emanating from the singularity if and only if there exist future-directed radial null geodesics emanating from the singularity. This result can be interpreted as indicating the robustness of previous results on radial geodesics, with respect to the presence of angular momentum.

Geometry and topology of singularities in spherical dust collapse

We derive some more results on the nature of the singularities arising in the collapse of inhomogeneous dust spheres. (i) It is shown that there are future-pointing radial and non-radial time-like geodesics emerging from the singularity if and only if there are future-pointing radial null geodesics emerging from the singularity. (ii) Limits of various spacetime invariants and other useful quantities (relating to Thornes point–cigar–barrel–pancake classification and to isotropy/entropy measures) are studied in the approach to the singularity. (iii) The topology of the singularity is studied from the point of view of ideal boundary structure. In each case, the different nature of the visible and censored region of the singularity is emphasized.

Review on exact and perturbative deformations of the Einstein–Straus model: uniqueness and rigidity results

The Einstein–Straus model consists of a Schwarzschild spherical vacuole in a Friedman–Lemaître–Robertson–Walker (FLRW) dust spacetime (with or without

Relative information entropy in cosmology: The problem of information entanglement

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