Anomaly-free deformations of spherical general relativity coupled to matter

TL;DR

This paper develops a systematic method for constructing spherically symmetric models of general relativity with matter, incorporating holonomy modifications while maintaining covariance, and presents a regular covariant polymeric model with physical implications.

Contribution

It introduces a family of anomaly-free, covariant Hamiltonian models with holonomy corrections in matter-coupled spherical gravity, extending previous approaches with a new systematic framework.

Findings

Explicit form of deformed Hamiltonian with free functions

Identification of a weak observable interpreted as mass

Presentation of a regular covariant polymeric model

Abstract

A systematic approach is developed in order to obtain spherically symmetric midisuperspace models that accept holonomy modifications in the presence of matter fields with local degrees of freedom. In particular, starting from the most general Hamiltonian quadratic in radial derivatives of the variables, we obtain a family of effective modified constraints that satisfy Dirac's deformation algebra, which encodes the covariance of general relativity, and show that (scale-dependent) holonomy corrections can be consistently implemented. In vacuum, the deformed anomaly-free Hamiltonian is explicitly written in terms of three free functions and we obtain a weak observable that can be interpreted as the mass of the model. Finally, as a particular example, we present a specific covariant polymeric model that remains regular for any value of the connection components. Some of its physical implications and the relation with previous studies in the literature are commented.