Mass and Horizon Dirac Observables in Effective Models of Quantum Black-to-White Hole Transition

TL;DR

This paper explores the role of mass and horizon Dirac observables in effective loop quantum gravity models of black-to-white hole transitions, revealing new models and relations between observables and quantum effects.

Contribution

It introduces a new polymerization model that overcomes previous initial condition restrictions and clarifies the role of Dirac observables in quantum black hole models.

Findings

Existence of two relevant Dirac observables linked to black and white hole masses.

A new polymerization model allows for broader initial conditions.

Quantum effects impose a universal curvature bound, independent of mass relations.

Abstract

In the past years, black holes and the fate of their singularity have been heavily studied within loop quantum gravity. Effective spacetime descriptions incorporating quantum geometry corrections are provided by the so-called polymer models. Despite the technical differences, the main common feature shared by these models is that the classical singularity is resolved by a black-to-white hole transition. In a recent paper, we discussed the existence of two Dirac observables in the effective quantum theory respectively corresponding to the black and white hole mass. Physical requirements about the onset of quantum effects then fix the relation between these observables after the bounce, which in turn corresponds to a restriction on the admissible initial conditions for the model. In the present paper, we discuss in detail the role of such observables in black hole polymer models. First, we revisit previous models and analyse the existence of the Dirac observables there. Observables for the horizons or the masses are explicitly constructed. In the classical theory, only one Dirac observable has physical relevance. In the quantum theory, we find a relation between the existence of two physically relevant observables and the scaling behaviour of the polymerisation scales under fiducial cell rescaling. We present then a new model based on polymerisation of new variables which allows to overcome previous restrictions on initial conditions. Quantum effects cause a bound of a unique Kretschmann curvature scale, independently of the relation between the two masses.