An effective model for the quantum Schwarzschild black hole

Alonso-Bardaji, Asier; Brizuela, David; Vera, Raül

doi:10.1016/j.physletb.2022.137075

Cited by 40 publications

(26 citation statements)

References 23 publications

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“…Following the anomaly-free polymerization presented in [24] both for vacuum and matter fields with local degrees of freedom, in this paper we study the physical implications of such model in the vacuum case, extending and completing the results announced in [23]. We show, in particular, that the polymerization, which can be achieved by performing a certain canonical transformation and linear combination of classical constraints, can be naturally associated to a geometry, ensuring that gauge transformations on phase space correspond to coordinate transformations on the spacetime solution.…”

Section: Introductionsupporting

confidence: 63%

“…The gauge freedom inherent to the problem allows to fix two relations (gauge choice) between the functions on phase space. For each gauge choice the solution to the system of equations (11) will yield a corresponding line element of the form (23). Since our construction is consistent, different gauge choices will simply lead to different charts (with different domains in M in general) and corresponding expressions (line elements) for the same metric, thus providing a unique spacetime solution.…”

Section: The Solution In Different Domainsmentioning

confidence: 99%

“…In this section we start with the chart {t, x} (plus the angular coordinates) on some domain of M in which the metric tensor g is given by the line element (23). The gauge freedom inherent to the problem allows to fix two relations (gauge choice) between the functions on phase space.…”

Section: The Solution In Different Domainsmentioning

confidence: 99%

“…Explicitly, the domain D S of the chart Ψ D S = { t, r} on M is only restricted by r ∈ (2m, ∞). The line element (23) in this chart thus reads…”

Section: A Static Regionmentioning

confidence: 99%

“…Some vacuum studies following the consistent constraint deformation approach predict the formation of an Euclidean region in the deep quantum regime [20], where the notion of causality would be lost. This result shows that a priori geometry should not be assumed but rather derived from the modified phase space [14,[20][21][22][23].…”

Section: Introductionmentioning

confidence: 98%

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Nonsingular spherically symmetric black-hole model with holonomy corrections

Alonso-Bardaji,

Brizuela,

Vera

2022

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We present a covariant model of a spherically symmetric black hole with corrections motivated by loop quantum gravity. The effective modifications, parametrized by a positive constant λ, are implemented through a canonical transformation and a linear combination of the constraints of general relativity, in such a way that the theory remains free of anomalies and general relativity is recovered for λ = 0. In addition, the corresponding metric is constructed in a fully covariant way to ensure that gauge transformations on phase space correspond to coordinate changes. The solution for each gauge choice provides a chart and corresponding line element of a spacetime solution whose geometry is unambiguously determined in terms of the parameter λ and a constant of motion m. For positive values of m, the solution is asymptotically flat and contains a globally hyperbolic black-hole/white-hole region with a minimal spacelike hypersurface that replaces the Schwarzschild singularity. The corresponding exterior regions are isometric and, in particular, allow the computation of the ADM mass. The procedure to obtain the global causal structure of the solution yields, also, its maximal analytic extension.

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Section: Introductionsupporting

confidence: 63%

Section: The Solution In Different Domainsmentioning

confidence: 99%

Section: The Solution In Different Domainsmentioning

confidence: 99%

“…Explicitly, the domain D S of the chart Ψ D S = { t, r} on M is only restricted by r ∈ (2m, ∞). The line element (23) in this chart thus reads…”

Section: A Static Regionmentioning

confidence: 99%