Global Structure of Exact Scalar Hairy Dynamical Black Holes

TL;DR

This paper investigates the global structure and evolution of exact scalar hairy dynamical black holes in Einstein gravity, analyzing horizon behavior, late-time states, and introducing charged solutions with Maxwell fields to understand charge effects.

Contribution

It provides new insights into the formation and late-time behavior of scalar hairy black holes, including charged solutions with non-minimal coupling, expanding understanding of dynamical black hole structures.

Findings

Apparent and event horizons monotonically increase with advanced time.

At late times, horizons approach each other and become future outer.

Electric charge significantly alters the dynamical evolution of the black holes.

Abstract

We study the global structure of some exact scalar hairy dynamical black holes which were constructed in Einstein gravity either minimally or non-minimally coupled to a scalar field. We find that both the apparent horizon and the local event horizon (measured in luminosity coordinate) monotonically increase with the advanced time as well as the Vaidya mass. At late advanced times, the apparent horizon approaches the event horizon and gradually becomes future outer. Correspondingly, the space-time arrives at stationary black hole states with the relaxation time inversely proportional to the $1/(n-1)$ power of the final black hole mass, where $n$ is the space-time dimension. These results strongly support the solutions describing the formation of black holes with scalar hair. We also obtain new charged dynamical solutions in the non-minimal theory by introducing an Maxwell field which is non-minimally coupled to the scalar. The presence of the electric charge strongly modifies the dynamical evolution of the space-time.