The Immirzi field in modified gravity: superentropic black holes with scalar hair

TL;DR

This paper explores how a dynamical Immirzi field in modified f(R) gravity influences black hole solutions, revealing superentropic black holes with scalar hair and modified entropy, while restoring standard quantum gravity behavior asymptotically.

Contribution

It introduces an analytic solution for asymptotically AdS black holes with scalar hair influenced by a dynamical Immirzi field in f(R) gravity.

Findings

Black holes exhibit scalar hair dependent on the Immirzi field.

The Immirzi field modifies the black hole entropy law.

The solution violates the reverse isoperimetric inequality, indicating superentropic behavior.

Abstract

In the context of f(R) generalizations to the Holst action, endowed with a dynamical Immirzi field, we derive an analytic solution describing asymptotically anti-de Sitter black holes with hyperbolic horizon. These exhibit a scalar hair of the second kind which ultimately depends on the Immirzi field radial behaviour. In particular, we show how the Immirzi field modifies the usual entropy law associated to the black hole. We also verify that the Immirzi field boils down to a constant value in the asymptotic region, thus restoring the standard loop quantum gravity picture. We finally prove the violation of the reverse isoperimetric inequality, resulting in the superentropic nature of the black hole, and we discuss in detail the thermodynamic stability of the solution.