Some Properties of Domain Wall Solution in the Randall-Sundrum Model

TL;DR

This paper investigates the properties of domain wall solutions in the Randall-Sundrum model, analyzing their stability, curvature, and behavior through analytical and numerical methods, and presents exact solutions illustrating singularity resolution.

Contribution

It provides a detailed analysis of domain wall solutions in the Randall-Sundrum model, including stability, curvature properties, and exact solutions with singularities.

Findings

Bulk curvature changes sign around the wall surface.

Domain wall solutions can resolve singularities present in exact solutions.

The solutions exhibit specific behaviors of warp factor and Higgs field.

Abstract

Properties of the domain wall (kink) solution in the 5 dimensional Randall-Sundrum model are examined both {\it analytically} and {\it numerically}. The configuration is derived by the bulk Higgs mechanism. We focus on 1) the convergence property of the solution, 2) the stableness of the solution, 3) the non-singular property of the Riemann curvature, 4) the behaviours of the warp factor and the Higgs field. It is found that the bulk curvature changes the sign around the surface of the wall. We also present some {\it exact} solutions for two simple cases: a) the no potential case, b) the cosmological term dominated case. Both solutions have the (naked) curvature singularity. We can regard the domain wall solution as a singularity resolution of the exact solutions.