Loop quantization of spherically symmetric midi-superspaces

TL;DR

This paper presents a loop quantum gravity quantization of spherically symmetric vacuum spacetimes, simplifying the constraints and exploring implications for more general models using the uniform discretization approach.

Contribution

It introduces a loop quantization method for spherically symmetric midi-superspaces, addressing constraint reduction and dynamics in a simplified setting.

Findings

Successfully quantized the exterior of spherically symmetric vacuum spacetimes

Eliminated the diffeomorphism constraint via partial gauge fixing

Discussed potential issues in more general models with uniform discretization

Abstract

We quantize the exterior of spherically symmetric vacuum space-times using a midi-superspace reduction within the Ashtekar new variables. Through a partial gauge fixing we eliminate the diffeomorphism constraint and are left with a Hamiltonian constraint that is first class. We complete the quantization in the loop representation. We also use the model to discuss the issues that will arise in more general contexts in the ``uniform discretization'' approach to the dynamics.