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

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.

Breaking of isospectrality of quasinormal modes in nonrotating loop quantum gravity black holes

“…Despite all that, we expect that our results are robust regarding the breaking of isospectrality, which is the main result of this manuscript. Besides, although we have considered just a few effective geometries, we expect that isospectrality will also be broken in other black hole effective geometries [31,[42][43][44][45].…”

Two-time alternative to the Ashtekar-Olmedo-Singh black hole interior

“…Nevertheless, the authors of Ref. [47] have indicated that this makes the relation between the proposed Hamiltonian and the dynamical equations unclear, given that an extra phase space dependent factor would enter the equations of motion should the non-trivial nature of the polymerization parameters be taken into account, leading to a more involved dynamics [47,48].…”

“…In view of this situation, and focusing exclusively on the Hamiltonian derivation of the AOS solution, an alternative approach has been proposed in Ref. [48] to obtain the dynamical equations while considering the non-commutativity of the polymerization parameters with the canonical variables, bringing together a treatment of these parameters as true constants of motion and the undoubtedly interesting physical results of the original AOS model. In that paper, we introduced an alternative prescription for the selection of the polymerization parameters that extends the ideas of Ref.…”

“…After reabsorbing those factors via time redefinitions and obtaining the form of the dynamical solutions, we discussed in Ref. [48] some consequences of the relation between the newly-defined times and their behavior in the asymptotic limit of infinitely large black hole masses. The effective spacetime geometry derived with this procedure is fundamentally different from that in the original works.…”

“…The objetive of the present work is to develop the preliminary ideas introduced in Ref. [48] and, in particular, to address the issue of whether there exists any obstruction to our proposal such as it was originally formulated, with special emphasis on a good behavior of all the interior geometry. This step is vital if we want to examine the physical properties of the model at a later point, in order to fully comprehend the effective theory and set it on a firm foundation on top of which one may complete the quantization program.…”