Spherical Domain Wall Collapse in a Dust Universe

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-Lemaître-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 Lemaître-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 $M_{\mathrm{BH}}\simeq 17\sigma /H_{\mathrm{hc}}$, where $H_{\mathrm{hc}}$ 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.

26 pages, 9 figures, estimate of black hole mass is corrected

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