Thick de Sitter 3-Branes, Dynamic Black Holes and Localization of Gravity

TL;DR

This paper investigates thick de Sitter 3-branes embedded in a five-dimensional bulk with scalar fields, revealing solutions that localize gravity and feature a universal mass gap separating graviton modes.

Contribution

It provides exact solutions for thick de Sitter 3-branes with black hole or Rindler-like geometries and demonstrates gravity localization with a stable scalar perturbation analysis.

Findings

Gravity is localized near the brane.

A zero graviton mode exists with a mass gap.

Scalar perturbations are stable.

Abstract

The embedding of a thick de Sitter 3-brane into a five-dimensional bulk is studied, assuming a scalar field with potential is present in the bulk. A class of solutions is found in closed form that can represent a thick de Sitter 3-brane interpolating either between two dynamical black holes with a $R \times S_{4}$ topology or between two Rindler-like spacetimes with a $R_{2}\times S_{3}$ topology. The gravitational field is localized in a small region near the center of the 3-brane. The analysis of graviton fluctuations shows that a zero mode exists and separates itself from a set of continuous modes by a mass gap. The existence of such a mass gap is shown to be universal. The scalar perturbations are also studied and shown to be stable.