Non-minimal couplings, quantum geometry and black hole entropy

TL;DR

This paper extends loop quantum gravity calculations of black hole entropy to include non-minimally coupled scalar fields, showing that the quantum geometry remains consistent and the entropy formula aligns with classical predictions.

Contribution

It introduces a method to incorporate non-minimal scalar couplings into quantum geometry calculations of black hole entropy within loop quantum gravity.

Findings

Quantum geometry remains consistent with non-minimal couplings.

Black hole entropy depends on scalar fields as predicted by classical laws.

The Barbero-Immirzi parameter remains unchanged from the minimal coupling case.

Abstract

The black hole entropy calculation for type I isolated horizons, based on loop quantum gravity, is extended to include non-minimally coupled scalar fields. Although the non-minimal coupling significantly modifies quantum geometry, the highly non-trivial consistency checks for the emergence of a coherent description of the quantum horizon continue to be met. The resulting expression of black hole entropy now depends also on the scalar field precisely in the fashion predicted by the first law in the classical theory (with the same value of the Barbero-Immirzi parameter as in the case of minimal coupling).