No-go theorem for false vacuum black holes

TL;DR

This paper proves a no-go theorem showing that non-singular black hole solutions with a scalar field transitioning from a false vacuum at the center to a true vacuum at infinity cannot exist within classical general relativity.

Contribution

It extends a no-hair theorem to the black hole interior, demonstrating the impossibility of smooth interpolating solutions with a scalar field in this setup.

Findings

No smooth solutions interpolate between de Sitter and Schwarzschild regions.

Non-singular false vacuum black holes are not possible under the given conditions.

The theorem constrains models of black holes with scalar fields and vacuum transitions.

Abstract

We study the possibility of non-singular black hole solutions in the theory of general relativity coupled to a non-linear scalar field with a positive potential possessing two minima: a `false vacuum' with positive energy and a `true vacuum' with zero energy. Assuming that the scalar field starts at the false vacuum at the origin and comes to the true vacuum at spatial infinity, we prove a no-go theorem by extending a no-hair theorem to the black hole interior: no smooth solutions exist which interpolate between the local de Sitter solution near the origin and the asymptotic Schwarzschild solution through a regular event horizon or several horizons.