Black hole solutions in modified gravity induced by quantum metric fluctuations

TL;DR

This paper explores how quantum metric fluctuations influence black hole solutions in modified gravity, revealing their impact on black hole formation, structure, and thermodynamics through numerical analysis.

Contribution

It introduces a model where quantum fluctuations are represented by a scalar field coupled to the metric, and analyzes their effects on black hole solutions and thermodynamic properties.

Findings

Quantum fluctuations induce singularities indicating black hole formation.

Different scalar potential models affect black hole thermodynamics.

Black hole evaporation times are computed considering quantum corrections.

Abstract

The inclusion of the quantum fluctuations of the metric in the geometric action is a promising avenue for the understanding of the quantum properties of gravity. In this approach the metric is decomposed in the sum of a classical and of a fluctuating part, of quantum origin, which can be generally expressed in terms of an arbitrary second order tensor, constructed from the metric, and from the thermodynamic quantities describing matter fields. In the present paper we investigate the effects of the quantum fluctuations on the spherically symmetric static black hole solutions of the modified field equations, obtained from a variational principle, by assuming that the quantum correction tensor is given by the coupling of a scalar field to the metric tensor. After reformulating the field equations in a dimensionless form, and by introducing a suitable independent radial coordinate, we obtain their solutions numerically. We detect the formation of a black hole from the presence of a singularity in the metric tensor components. Several models, corresponding to different functional forms of the scalar field potential, are considered. The thermodynamic properties of the black hole solutions (horizon temperature, specific heat, entropy and evaporation time due to Hawking luminosity) are also investigated.