Coherent States for Black Holes

TL;DR

This paper constructs coherent states for Schwarzschild black holes within canonical quantum gravity, revealing how quantum fluctuations depend on proximity to the horizon and suggesting a discrete structure near the singularity.

Contribution

It introduces a method to define coherent states for black holes in canonical quantum gravity, capturing horizon information and quantum fluctuations.

Findings

Quantum fluctuations depend on distance from the horizon

Near the singularity, space appears discrete

Singularity is excluded from the spectrum for small black holes

Abstract

We determine coherent states peaked at classical space-time of the Schwarzschild black hole in the frame-work of canonical quantisation of general relativity. The information about the horizon is naturally encoded in the phase space variables, and the perturbative quantum fluctuations around the classical geometry depend on the distance from the horizon. For small black holes, space near the vicinity of the singularity appears discrete with the singular point excluded from the spectrum.