The dynamics of curved gravitating walls

TL;DR

This paper investigates the dynamics of self-gravitating domain walls within the $$ model, demonstrating that Nambu motion is dominant and analyzing how gravity influences wall behavior, including retardation of collapse in spherical cases.

Contribution

It provides an analytical study of gravity's effect on domain wall dynamics, extending the understanding of Nambu motion corrections in curved spacetime.

Findings

Nambu motion remains dominant even with gravity.

Gravity slows down the collapse of spherical walls.

Analytical corrections to idealized motion are derived.

Abstract

We examine the dynamics of a self-gravitating domain wall using the $\lambda \Phi^4$ model as a specific example. We find that the Nambu motion of the wall is quite generic and dominates the wall motion even in the presence of gravity. We calculate the corrections to this leading order motion, and estimate the effect of the inclusion of gravity on the dynamics of the wall. We then treat the case of a spherical gravitating thick wall as a particular example, solving the field equations and calculating the corrections to the Nambu motion analytically for this specific case. We find that the presence of gravity retards collapse in this case.