Non-Minimally Coupled Scalar Field, Area Quantization and Black Hole Entropy

TL;DR

This paper derives the discrete area spectrum of black hole horizons in a theory with scalar fields non-minimally coupled to gravity, showing it depends on the scalar field and Barbero-Immirzi parameter, and supports the Bekenstein-Mukhanov proposal.

Contribution

It provides a derivation of the horizon area spectrum for black holes in a non-minimally coupled scalar field theory using horizon symmetry algebra, independent of specific quantum gravity models.

Findings

Area spectrum is equidistant and depends on scalar field and Barbero-Immirzi parameter.

Spectrum derivation is based on horizon symmetry algebra, not a specific quantum gravity theory.

Supports the Bekenstein-Mukhanov quantization proposal for black hole entropy.

Abstract

The enumeration of black hole entropy in candidate theories of quantum gravity utilises the quantum properties of microstates residing on the black hole horizon. For example, in Loop Quantum Gravity, the computation of entropy is based on the spectrum of area operator, and one determines the possible number of area mirocrostates corresponding to a given classical horizon area. In this paper, we derive the eigenspectrum of the horizon area operator for rotating/non-rotating black holes in a gravitational theory non-minimally coupled to scalar fields. Using the weak isolated horizon formalism, we show that the spectrum of area operator follows unambiguously from the algebra of horizon symmetry. More precisely, from the quantum mechanical point of view, the horizon geometry must be naturally discrete, a conclusion which is arrived at directly, without the need for any particular theory of quantum gravity. The area spectrum depends on the Barbero-Immirzi parameter as well as the value of scalar field on horizon. The area spectrum is equidistant, which is consistent with the Bekenstein-Mukhanov proposal and gives rise to black hole entropy and their quantum corrections.