PHYSICS SEMINAR
STELLAR ASTROPHYSICS & RELATIVITY RESEARCH CLUSTER SEMINAR
Lemaitre-Tolman-Bondi Spherical Solutions in General Relativity
Dr. Ivana Bochicchio
Department of Mathematics
University of Salerno (Italy)
Tuesday, June 29, 2010
2:00 pm
Nicolls 1
The Lemaıtre-Tolman-Bondi (LTB) models are spherically symmetric cosmological solutions of the Einstein equations where the matter source is a perfect fluid with zero pressure (“dust”), usually inhomogeneous in the radial direction. The importance of such Universes in relativistic cosmology is mainly based on the following observation: even if the Friedmann-Robertson-Walker (FRW) models are widely accepted to describe the cosmic evolution, more realistic universes include singularities, horizons, inhomogeneities observed from galactic to supercluster scales. The goal of the LTB approach is to describe cosmic inhomogeneities together with the overall cosmic dynamics.
The problem of LTB models in General Relativity has been tackled by Lemaitre and, afterwards, by Tolman and Bondi who formalized Lemaitre's results for dust (p=0), presenting all the exact solutions. We show that their parametric form can be obtained considering the limiting rectilinear solutions of the Newtonian Kepler problem. In addition, the analogy between the relativistic evolution of LTB shells and the classical discussion of a body falling in a Newtonian centre of attraction allows us to classify the orbits of each r-shell. In other words, it is possible to predict qualitatively the evolution of the LTB spacetimes using the classical Weierstrass approach. In a simple way, we can sketch the behavior of the shell with respect to the metric, the curvature, and hence the cosmological constant. We are then able to describe qualitatively and classify the possible types of evolution of the LTB-models keeping direct control of the dynamics.
