Staticity Theorem for Non-Rotating Black Holes with Non-Minimally Coupled Self-Interacting Scalar Fields

TL;DR

This paper proves that non-rotating black holes with non-minimally coupled scalar fields have a static domain of outer communication, extending understanding of scalar field configurations in black hole spacetimes.

Contribution

It establishes a staticity theorem for black holes with non-minimally coupled scalar fields, showing that such configurations lead to static spacetime regions.

Findings

Analytical scalar field configurations result in static domains of outer communication.

The study extends staticity results to non-minimally coupled scalar fields.

Non-rotating black holes with these scalar fields are shown to have static exterior regions.

Abstract

Self-interacting scalar field configurations which are non-minimally coupled ($\zeta\neq0$) to the gravity of a strictly stationary black hole with non-rotating horizon are studied. It is concluded that for analytical configurations the corresponding domain of outer communications is static.