Stationary spacetimes with time-dependent real scalar fields

TL;DR

This paper extends static scalar field solutions in Einstein--Klein--Gordon theory to rotating and higher-dimensional cases, and proves a no-hair theorem for stealth scalar fields on Schwarzschild black holes.

Contribution

It generalizes Wyman's static solutions to rotating and higher-dimensional spacetimes and establishes a no-hair theorem for stealth scalar fields.

Findings

Perturbative rotating solutions with time-dependent scalar fields.

Exact extension of static solutions to arbitrary dimensions.

No-hair theorem for stealth scalar fields on Schwarzschild black holes.

Abstract

In 1981 Wyman classified the solutions of the Einstein--Klein--Gordon equations with static spherically symmetric spacetime metric and vanishing scalar potential. For one of these classes, the scalar field linearly grows with time. We generalize this symmetry noninheriting solution, perturbatively, to a rotating one and extend the static solution exactly to arbitrary spacetime dimensions. Furthermore, we investigate the existence of nonminimally coupled, time-dependent real scalar fields on top of static black holes, and prove a no-hair theorem for stealth scalar fields on the Schwarzschild background.