Planar domain walls in black hole spacetimes

TL;DR

This study numerically examines how low-mass planar domain walls in a scalar field model interact with Schwarzschild and Kerr black holes, revealing their stability and dynamic behavior during black hole transit.

Contribution

It provides the first detailed numerical analysis of domain wall behavior in black hole spacetimes, including stability and mode ringing effects.

Findings

Domain walls exhibit ringing modes during black hole transit.

Perturbations diminish over time, indicating stability.

Behavior is consistent across different black hole types.

Abstract

We investigate the behaviour of low-mass, planar domain walls in the so-called $\phi^4$ model of the scalar field on the Schwarzschild and Kerr backgrounds. We focus on a transit of a domain wall through a black hole and solve numerically the equations of motion for a range of parameters of the domain wall and the black hole. We observe a behavior resembling an occurrence of ringing modes. Perturbations of domain walls vanish during latter evolution, suggesting their stability against a passage through the black hole. The results obtained for Kerr and Reissner-Nordstr\"om black holes are also compared.