Semiclassical quantisation of space-times with apparent horizons

TL;DR

This paper develops a semiclassical approach in quantum gravity to describe Schwarzschild and related space-times, deriving entropy, resolving singularities, and analyzing horizon properties.

Contribution

It introduces a method to derive Bekenstein-Hawking entropy from coherent states and extends the analysis to spherically symmetric apparent horizons.

Findings

Bekenstein-Hawking entropy obtained from the density matrix.

Singularity in curvature operator is resolved.

Results generalized to space-times with apparent horizons.

Abstract

Coherent or semiclassical states in canonical quantum gravity describe the classical Schwarzschild space-time. By tracing over the coherent state wavefunction inside the horizon, a density matrix is derived. Bekenstein-Hawking entropy is obtained from the density matrix, modulo the Immirzi parameter. The expectation value of the area and curvature operator is evaluated in these states. The behaviour near the singularity of the curvature operator shows that the singularity is resolved. We then generalise the results to space-times with spherically symmetric apparent horizons.