Spherically symmetric false vacuum: no-go theorems and global structure

TL;DR

This paper classifies all possible causal structures in static, spherically symmetric scalar field configurations in general relativity, showing that regular black holes with certain asymptotics are impossible and identifying conditions for soliton solutions.

Contribution

It provides a comprehensive classification of spacetime causal structures for scalar fields in GR and proves the non-existence of regular black holes with flat or AdS asymptotics in this setting.

Findings

Regular black holes with flat or AdS asymptotics are not possible.

Only solitons with a regular center and negative potentials are globally regular.

The classification applies to arbitrary scalar potentials, including non-positive-definite ones.

Abstract

We enumerate all possible types of spacetime causal structures that can appear in static, spherically symmetric configurations of a self-gravitating, real, nonlinear, minimally coupled scalar field \phi in general relativity, with an arbitrary potential V(\phi), not necessarily positive-definite. It is shown that a variable scalar field adds nothing to the list of possible structures with a constant \phi field, namely, Minkowski (or AdS), Schwarzschild, de Sitter and Schwarzschild - de Sitter. It follows, in particular, that, whatever is V(\phi), this theory does not admit regular black holes with flat or AdS asymptotics. It is concluded that the only possible globally regular, asymptotically flat solutions are solitons with a regular center, without horizons and with at least partly negative potentials V(\phi). Extension of the results to more general field models is discussed.