Primordial black hole formation from collapsing domain walls with full general relativity

Abstract

We study the dynamics of isolated closed domain walls with 3+1 numerical relativity. A closed wall shrinks due to its own surface tension, and its surface energy is converted to the kinetic energy, leading to implosion. Then, it can result in the formation of a black hole. First, we focus on spherically symmetric closed domain walls and clarify whether they finally evolve into black holes. Naively, the wall can collapse if its thickness is smaller than the Schwarzschild radius which is determined by the initial surface energy. Our numerical results support this naive criterion for the black hole formation, and indicate that more than 80% of the initial wall energy falls into the black hole. We also investigate the nonspherical collapse by considering the ellipsoidal configurations for the closed domain walls, and it turns out that black holes can be formed even when the ratio of semi-major to semi-minor axes is 1.5.