Evolving black hole with scalar field accretion

TL;DR

This paper derives approximate analytical solutions for dynamical black holes with scalar field accretion near the horizon, generalizing the Bondi formula and analyzing near-equilibrium dynamics.

Contribution

It introduces a new parametrization of the metric near the horizon and provides a general equation for accretion rate applicable to various scalar potentials and asymptotics.

Findings

Derived approximate solutions near the horizon for scalar field accretion.

Generalized the Bondi accretion formula for dynamical black holes.

Showed that purely ingoing flux solutions do not reach equilibrium.

Abstract

We obtain approximate analytical solutions of the Einstein equations close to the trapping horizon for a dynamical spherically symmetric black hole in the presence of a minimally coupled self-interacting scalar field. This is made possible by a new parametrization of the metric, in which the displacement from the horizon as well as its expansion rate feature explicitly. Our results are valid in a neighbourhood of the horizon and hold for any scalar field potential and spacetime asymptotics. An exact equation for the accretion rate is also obtained, which generalizes the standard Bondi formula. We also develop a dynamical system approach to study near-equilibrium black holes; using this formalism, we focus on a simple model to show that the near-equilibrium dynamics is characterised by scaling relations among dynamical variables. Moreover, we show that solutions with purely ingoing energy-momentum flux never reach equilibrium.