Stationary Vacuum Bubble in a Kerr-de Sitter Spacetime

TL;DR

This paper investigates false vacuum decay in a Kerr-de Sitter black hole spacetime, showing that black hole spin suppresses decay rates, and introduces a method to estimate decay parameters despite some geometric inconsistencies.

Contribution

It develops a framework for analyzing stationary vacuum bubbles in rotating black hole spacetimes using junction conditions and quasi-local energy, accounting for black hole spin effects.

Findings

Black hole spin suppresses false vacuum decay.

A method to estimate decay parameters with Kerr geometry assumptions.

Quantitative evaluation of geometric inconsistencies via Brown-York energy.

Abstract

We study false vacuum decay in a black hole (BH) spacetime with an angular momentum. Considering the false vacuum region described by a Kerr-de Sitter geometry, under the thin wall approximation, we can obtain the stationary configuration of the vacuum bubble seen from the outside false vacuum region without specifying the geometry inside the domain wall. Then, assuming the true vacuum region is described by a Kerr geometry, we can fix the mass and the spin parameter for the Kerr geometry by imposing the 1st junction conditions and conservation of the angular momentum. Although the assumption of the Kerr geometry inside the domain wall cannot be fully consistent with the 2nd junction conditions, we can roughly evaluate the error associated with this inconsistency by calculating the Brown-York quasi-local energy on the domain wall. Then the decay rate can be estimated by using the obtained parameters for the inside Kerr geometry and the Brown-York quasi-local energy. Our results support the statement that the BH spin suppresses the false vacuum decay in a BH spacetime.