The thermodynamics of isolated horizons in loop quantum gravity

TL;DR

This paper investigates the thermodynamics of isolated horizons within loop quantum gravity, deriving entropy and thermodynamic quantities consistent with Hawking's semiclassical results, and determining the Immirzi parameter for different dimensions.

Contribution

It introduces a microcanonical ensemble approach to isolated horizons in loop quantum gravity and calculates the Immirzi parameter for higher and 4D U(1) cases.

Findings

Black hole entropy matches Hawking's semiclassical analysis

Immirzi parameter values are obtained for various dimensions

Thermodynamical quantities are consistent with established physics

Abstract

The statistical mechanical calculation of the thermodynamical properties of non-rotating isolated horizons are studied in the loop quantum gravity framework. By employing the Hawking temperature and horizon mass of isolated horizons as physical inputs, the microcanonical ensemble associated with the system are well established. As a result, the black hole entropy and other thermodynamical quantities can be computed and consistent with well-known Hawking's semiclassical analysis. Moreover, the value of the Immirzi parameter of loop quantum gravity for {higher dimensional case and 4-dimensional U(1) case are} also obtained.