Critical behavior of spherically symmetric domain wall collapse

TL;DR

This paper investigates the critical collapse of spherically symmetric domain walls made of a scalar field with a double well potential, confirming Type II critical behavior and mass scaling in a full general relativistic numerical setting.

Contribution

It demonstrates the occurrence of Type II critical behavior in domain wall collapse with a double well potential using a full numerical relativity approach, extending previous scalar field studies.

Findings

Confirmed Type II critical behavior in domain wall collapse.

Observed mass and curvature scaling consistent with scalar field cases.

Validated the scaling index matches the massless scalar field scenario.

Abstract

Critical collapse of a spherically symmetric domain wall is investigated. The domain wall is made of a minimally coupled scalar field with a double well potential. We consider a sequence of the initial data which describe a momentarily static domain wall characterized by its initial radius. The time evolution is performed by a full general relativistic numerical code for spherically symmetric systems. In this paper, we use the maximal slice gauge condition, in which spacelike time slices may penetrate the black hole horizon differently from other widely used procedures. In this paper, we consider two specific shapes of the double well potential, and observe the Type II critical behavior in both cases. The mass scaling, sub-critical curvature scaling, and those fine structures are confirmed. The index of the scaling behavior agrees with the massless scalar case.