Spikes in Cosmic Crystallography II: Topological Signature of Compact Flat Universes

We study the topological signature of euclidean isometries in pair separations histograms (PSH) and elucidate some unsettled issues regarding distance correlations between cosmic sources in cosmic crystallography. Reducing the noise of individual PSH's using mean pair separations histograms we show how to distinguish between topological and statistical spikes. We report results of simulations that evince that topological spikes are not enough to distinguish between manifolds with the same set of Clifford translations in their covering groups, and that they are not the only signature of topology in PSH's corresponding to euclidean small universes. We also show how to evince the topological signature due to non-translational isometries.Comment: 15 pages, 5 figures, LaTeX2e; Added 2 references and inserted clarifying details. To appear in Phys. Lett. A (2000) in the present for

An anisotropic cosmological model with isotropic background radiation

We present an exact solution of Einstein equations that describes a Bianchi type III spacetime with conformal expansion. The matter content is given by an anisotropic scalar field and two perfect fluids representing dust and isotropic radiation. Based on this solution, we construct a cosmological model that respects the evolution of the scale factor predicted in standard cosmology.Comment: 4 pages; contribution to the Proceedings of the 24th Spanish Relativity Meeting (ERE2001

Energy-momentum and angular momentum of Goedel universes

We discuss the Einstein energy-momentum complex and the Bergmann-Thomson angular momentum complex in general relativity and calculate them for space-time homogeneous Goedel universes. The calculations are performed for a dust acausal model and for a scalar-field causal model. It is shown that the Einstein pseudotensor is traceless, not symmetric, the gravitational energy is "density" is negative and the gravitational Poynting vector vanishes. Significantly, the total (gravitational and matter) energy "density" fro the acausal model is zero while for the casual model it is negative.The Bergmann-Thomson angular momentum complex does not vanish for both G\"odel models.Comment: an amended version, 24 pages, accepted to PR

Detectability of Cosmic Topology in Flat Universes

Recent observations seem to indicate that we live in a universe whose spatial sections are nearly or exactly flat. Motivated by this we study the problem of observational detection of the topology of universes with flat spatial sections. We first give a complete description of the diffeomorphic classification of compact flat 3-manifolds, and derive the expressions for the injectivity radii, and for the volume of each class of Euclidean 3-manifolds. There emerges from our calculations the undetectability conditions for each (topological) class of flat universes. To illustrate the detectability of flat topologies we construct toy models by using an assumption by Bernshtein and Shvartsman which permits to establish a relation between topological typical lengths to the dynamics of flat models.Comment: 17 pages, 1 figure, latex2e. New references added. Inserted clarifying points. To appear in Phys. Lett. A (2003) in the present for

Godel brane

We consider the brane-world generalisation of the Godel universe and analyse its dynamical interaction with the bulk. The exact homogeneity of the standard Godel spacetime no longer holds, unless the bulk is also static. We show how the anisotropy of the Godel-type brane is dictated by that of the bulk and find that the converse is also true. This determines the precise evolution of the nonlocal anisotropic stresses, without any phenomenological assumptions, and leads to a self-consistent closed set of equations for the evolution of the Godel brane. We also examine the causality of the Godel brane and show that the presence of the bulk cannot prevent the appearance of closed timelike curves.Comment: Revised version, to match paper published in Phys. Rev.

Limits of the Energy-Momentum Tensor in General Relativity

A limiting diagram for the Segre classification of the energy-momentum tensor is obtained and discussed in connection with a Penrose specialization diagram for the Segre types. A generalization of the coordinate-free approach to limits of Paiva et al. to include non-vacuum space-times is made. Geroch's work on limits of space-times is also extended. The same argument also justifies part of the procedure for classification of a given spacetime using Cartan scalars. pacs numbers: 04.20.-q 04.20.Cv 04.20.Jb 1 Introduction The matter content in general relativity theory is described by a second order symmetric tensor, the energy-momentum tensor. Under limiting processes, one would like to know which energy-momentum tensors might arise. A step in this study is the investigation of the limits of classes of energy-momentum tensors. Departamento F'isica Te'orica, Universidade do Estado do Rio de Janeiro, Rua S~ao Francisco Xavier 524 (Maracan~a), 20550-013 Rio de Janeiro - RJ, Brasil, inte..