Radial kinks in a Schwarzschild-like geometry

TL;DR

This paper investigates the dynamics of a domain wall in a Schwarzschild-like gravitational environment, revealing that such walls tend to collapse towards the gravitational source, with an effective model accurately describing this behavior.

Contribution

It introduces an effective model for the dynamics of spherical domain walls in curved spacetime, applicable even for large gravitating masses, and analyzes their collapse behavior.

Findings

Spherical domain walls tend to collapse towards the gravitational source.

The effective model accurately describes the domain wall dynamics outside the perturbation region.

Collapse occurs regardless of the initial size of the domain wall.

Abstract

We study the propagation of a domain wall (kink) of the $\phi^4$ model in a radially symmetric environment defined by a gravity source. This source deforms the standard Euclidian metric into a Schwarzschild-like one. We introduce an effective model that accurately describes the dynamics of the kink center. This description works well even outside the perturbation region, i.e., even for large masses of the gravitating object. We observed that such a spherical domain wall surrounding a star-type object inevitably "collapses", i.e., shrinks in radius towards the origin and offer an understanding of the latter phenomenology. The relevant analysis is presented for a circular domain wall and a spherical one.