Astrophysical and Cosmological Consequences of the Dynamical Localization of Gravity

TL;DR

This thesis explores the astrophysical and cosmological implications of gravity localization in braneworld models, revealing new effects on star behavior, black holes, and universe evolution through holographic and higher-curvature theories.

Contribution

It introduces novel insights into braneworld effects on stars, black holes, and cosmology, including a non-static exterior for collapsing objects and the impact of Gauss-Bonnet terms.

Findings

Braneworld effects influence static star pressure matching.

Collapsing dust clouds exhibit non-static exteriors with energy flux.

Gauss-Bonnet terms modify the internal structure and cosmological dynamics.

Abstract

In this thesis I review cosmological and astrophysical exact models for Randall-Sundrum-type braneworlds and their physical implications. I present new insights and show their analogies with quantum theories via the holographic idea. In astrophysics I study the two fundamental models of a spherically symmetric static star and spherically symmetric collapsing objects. I show how matching for the pressure of a static star encodes braneworld effects. In addition I study the problem of the vacuum exterior conjecturing a uniqueness theorem. Furthermore I show that a collapsing dust cloud in the braneworld has a non-static exterior, in contrast to the General Relativistic case. This non-static behaviour is linked to the presence of a "surplus potential energy" that must be released, producing a non-zero flux of energy. Via holography this can be connected with the Hawking process, giving an indirect measure of the brane tension. In cosmology I investigate the generalization of the Randall-Sundrum-type model obtained by introducing the Gauss-Bonnet combination into the action. I elucidate the junction conditions necessary to study the brane model and obtain the cosmological dynamics, showing that, even in the thin shell limit for the brane, the Gauss-Bonnet term implies a non-trivial internal structure for the matter and geometry distributions. Independently of the gravitational theory used, I show how to derive the modified Friedman equation and how it is related to the black hole solution of the theory. Via holography I also show how to interpret quantum mechanically the mass of this black hole from a four-dimensional perspective in the simplest Randall-Sundrum-type scenario.