Interaction of a black hole with scalar field in cosmology background

TL;DR

This paper explores how a scalar field, representing dark energy, interacts with black holes in a cosmological setting, affecting black hole growth and scalar field behavior near horizons, with solutions showing stable late-time energy densities.

Contribution

It provides a perturbative analysis of black hole and scalar field interaction in a cosmological background, deriving solutions for the field, black hole mass, and expansion rate, highlighting stable late-time energy densities.

Findings

Scalar field energy density converges to a stable value at late times.

The scalar field can be made continuous and bounded on the horizon.

Derived solutions for scalar field, black hole mass, and expansion rate in cosmological background.

Abstract

Recent data from elliptical galaxies indicate that the growth in the masses of black holes exceeds what is expected from the accretion of surrounding matter, and this growth appears to be dependent on the expansion of the universe. This phenomenon can be explained by considering the accretion of dark energy, which is responsible for cosmological expansion, into these black holes. In this paper, we investigate the perturbative interaction of a black hole with a real scalar field $\phi$ (which can represent dark energy) in a cosmological background using an appropriate metric. We derive solutions for the field $\phi(t, r)$, the black hole mass $M(t)$, and the expansion rate $H(t)$, and discuss the behaviour of the scalar field $\phi$ in the vicinity of the black hole, with respect to exterior and interior observers. We obtain the energy density of $\phi$ inside of the black hole and find that energy density converges and tends to take a non-vanishing fixed values (stable) at late time of cosmological expansion. We find that on horizon surfaces, it is possible to make the field $\phi$ continuous and bounded (maybe differentiable) function.