Four-dimensional gravity on a thick domain wall

TL;DR

This paper investigates how four-dimensional gravity can emerge from a simple thick domain wall in AdS space, analyzing the spectrum of continuum modes and showing the absence of resonances.

Contribution

It provides a solvable model of a thick domain wall in AdS space and analyzes the spectrum of gravitational modes, clarifying the conditions for gravity localization.

Findings

No resonances in the continuum spectrum

The quantum mechanics problem can be solved in closed form

Supports understanding of gravity localization on domain walls

Abstract

We consider an especially simple version of a thick domain wall in $AdS$ space and investigate how four-dimensional gravity arises in this context. The model we consider has the advantage, that the equivalent quantum mechanics problem can be stated in closed form. The potential in this Schr\"odinger equation suggests that there could be resonances in the spectrum of the continuum modes. We demonstrate that there are no such resonances in the model we consider.