Spherical Domain Wall Collapse in a Dust Universe

TL;DR

This paper models the collapse of a spherical domain wall in a dust-filled universe, showing it leads to black hole formation with a universal mass relation and specific dust distribution, offering potential observational signatures.

Contribution

It provides a detailed dynamical analysis of domain wall collapse in an expanding universe, deriving universal black hole mass and dust density profiles post-collapse.

Findings

Black hole forms after domain wall collapse for any initial condition.

Black hole mass is approximately 17 times the tension divided by the Hubble parameter at horizon crossing.

Dust density near the center scales as R^{3/2} after collapse.

Abstract

To clarify observational consequence of bubble nucleations in inflationary era, we analyse dynamics of a spherical domain wall in an expanding universe. We consider a spherical shell of the domain wall with tension $\sigma$ collapsing in a spherically-symmetric dust universe, which is initially separated into the open Friedmann-Lema\^itre-Robertson-Walker universe inside the shell and the Einstein-de Sitter universe outside. The domain wall shell collapses due to the tension, and sweeps the dust fluid. The universe after the collapse becomes inhomogeneous and is described by the Lema\^itre-Tolman-Bondi model. We construct solutions describing this inhomogeneous universe by solving dynamical equations obtained from Israel's junction conditions applied to this system. We find that a black hole forms after the domain wall collapse for any initial condition, and that the black hole mass at the moment of its formation is universally given by $M_{\rm BH}\simeq 17 \sigma/H_{\rm hc}$, where $H_{\rm hc}$ is the Hubble parameter at the time when the shell radius becomes equal to the Hubble radius. We also find that the dust fluid is distributed as $\rho\propto R^{3/2}$ near the central region after the collapse, where $R$ is the area radius. These features would provide observable signatures of a spherical domain wall generated in the early universe.