Revisiting the quantum scalar field in spherically symmetric quantum gravity

TL;DR

This paper advances the understanding of spherically symmetric quantum gravity with a scalar field by applying uniform discretization and variational methods to extend previous loop quantum gravity results around Schwarzschild spacetime.

Contribution

It introduces a novel variational approach to minimize the discrete master constraint in loop quantum gravity for Schwarzschild spacetime with a scalar field.

Findings

Successful minimization of the discrete master constraint.

Construction of a vacuum state combining Fock vacuum and Gaussian centered on Schwarzschild.

Comparison with previous results by Gambini, Pullin, and Rastgoo.

Abstract

We extend previous results in spherically symmetric gravitational systems coupled with a massless scalar field within the loop quantum gravity framework. As starting point, we take the Schwarzschild spacetime. The results presented here rely on the uniform discretization method. We are able to minimize the associated discrete master constraint using a variational method. The trial state for the vacuum consists of a direct product of a Fock vacuum for the matter part and a Gaussian centered around the classical Schwarzschild solution. This paper follows the line of research presented by Gambini, Pullin and Rastgoo and a comparison between their result and the one given in this work is made.