Exploring Alternatives to the Hamiltonian Calculation of the Ashtekar-Olmedo-Singh Black Hole Solution

Alejandro García-Quismondo,Guillermo A Mena Marugán

doi:10.3389/fspas.2021.701723

Alejandro García-Quismondo, Guillermo A Mena Marugán

Open Access

https://doi.org/10.3389/fspas.2021.701723

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Abstract

In this article, we reexamine the derivation of the dynamical equations of the Ashtekar-Olmedo-Singh black hole model in order to determine whether it is possible to construct a Hamiltonian formalism where the parameters that regulate the introduction of quantum geometry effects are treated as true constants of motion. After arguing that these parameters should capture contributions from two distinct sectors of the phase space that had been considered independent in previous analyses in the literature, we proceed to obtain the corresponding equations of motion and analyze the consequences of this more general choice. We restrict our discussion exclusively to these dynamical issues. We also investigate whether the proposed procedure can be reconciled with the results of Ashtekar, Olmedo, and Singh, at least in some appropriate limit.

Highlights

Over two years ago, a new model to describe black hole spacetimes in effective loop quantum cosmology was put forward in (Ashtekar et al, 2018a; Ashtekar et al, 2018b; Ashtekar and Olmedo, 2020) by Ashtekar, Olmedo, and Singh (AOS)
Instead of choosing the relevant polymerization parameters as constants or as arbitrary phase space functions, they claim to fix them to be Dirac observables. They do not treat them as such in their Hamiltonian calculation: in practice, the polymerization parameters are regarded as constants in that calculation and, once the dynamical equations have been derived and solved, the parameters are set equal to the value of certain functions of the ADM mass of the black hole, which is a Dirac observable itself
We have examined whether it is possible to construct a Hamiltonian formalism where the polymerization parameters that encode the quantum corrections in black hole spacetimes can be treated as constants of motion

Summary

INTRODUCTION

A new model to describe black hole spacetimes in effective loop quantum cosmology was put forward in (Ashtekar et al, 2018a; Ashtekar et al, 2018b; Ashtekar and Olmedo, 2020) by Ashtekar, Olmedo, and Singh (AOS). Instead of choosing the relevant polymerization parameters as constants or as arbitrary phase space functions, they claim to fix them to be Dirac observables They do not treat them as such in their Hamiltonian calculation: in practice, the polymerization parameters are regarded as constants in that calculation and, once the dynamical equations have been derived and solved, the parameters are set equal to the value of certain functions of the ADM mass of the black hole, which is a Dirac observable itself. Throughout this article, we set the speed of light and the reduced Planck constant equal to one

DYNAMICAL EQUATIONS

TIME REDEFINITIONS

CONSISTENCY IN THE LIMIT OF LARGE BLACK HOLE MASSES

CONCLUSION

DATA AVAILABILITY STATEMENT