Covariance in self-dual inhomogeneous models of effective quantum geometry: Spherical symmetry and Gowdy systems

Achour, Jibril Ben; Brahma, Suddhasattwa

doi:10.1103/physrevd.97.126003

Cited by 27 publications

(26 citation statements)

References 112 publications

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“…[61][62][63] and Refs. [64][65][66] for extended discussions regarding the problem of covariance in such polymer constructions. junction conditions of GR [81].…”

Section: Introductionmentioning

confidence: 99%

Bouncing compact objects. Part I. Quantum extension of the Oppenheimer-Snyder collapse

Achour

Brahma

Uzan

2020

J. Cosmol. Astropart. Phys.

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This article proposes a generalization of the Oppenheimer-Snyder model which describes a bouncing compact object. The corrections responsible for the bounce are parameterized in a general way so as to remain agnostic about the specific mechanism of singularity resolution at play. It thus develops an effective theory based on a thin shell approach, inferring generic properties of such a UV complete gravitational collapse. The main result comes in the form of a strong constraint applicable to general UV models : if the dynamics of the collapsing star exhibits a bounce, it always occurs below, or at most at the energy threshold of horizon formation, so that only an instantaneous trapping horizon may be formed while a trapped region never forms. This conclusion relies solely on i) the assumption of continuity of the induced metric across the time-like surface of the star and ii) the assumption of a classical Schwarzschild geometry describing the (vacuum) exterior of the star. In particular, it is completely independent of the choice of corrections inside the star which leads to singularityresolution. The present model provides thus a general framework to discuss bouncing compact objects, for which the interior geometry is modeled either by a classical or a quantum bounce. In the latter case, our no-go result regarding the formation of trapped region suggests that additional structure, such as the formation of an inner horizon, is needed to build consistent models of matter collapse describing black-to-white hole bounces. Indeed, such additional structure is needed to keep quantum gravity effects confined to the high curvature regime, in the deep interior region, providing thus a new challenge for current constructions of quantum black-to-white hole bounce models. 4 In this model, the authors use the light-like version of the junction conditions discussed in Ref. [82]. 5 See Ref.[91] for a similar model.

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“…[61][62][63] and Refs. [64][65][66] for extended discussions regarding the problem of covariance in such polymer constructions. junction conditions of GR [81].…”

Section: Introductionmentioning

confidence: 99%

Bouncing compact objects. Part I. Quantum extension of the Oppenheimer-Snyder collapse

Achour

Brahma

Uzan

2020

J. Cosmol. Astropart. Phys.

Self Cite

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“…This construction was generalized to the Gowdy model and perturbative inhomogeneous cosmological background. Moreover, the polymerlike modifications can be implemented within theμ-scheme[56][57][58]. These results have been generalized recently in[59] 4.…”

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confidence: 99%

Deformed General Relativity and Quantum Black Holes Interior

2020

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Effective models of black holes interior have led to several proposals for regular black holes. In the so-called polymer models, based on effective deformations of the phase space of spherically symmetric general relativity in vacuum, one considers a deformed Hamiltonian constraint while keeping a non-deformed vectorial constraint, leading under some conditions to a notion of deformed covariance. In this article, we revisit and study further the question of covariance in these deformed gravity models. In particular, we propose a Lagrangian formulation for these deformed gravity models where polymer-like deformations are introduced at the level of the full theory prior to the symmetry reduction and prior to the Legendre transformation. This enables us to test whether the concept of deformed covariance found in spherically symmetric vacuum gravity can be extended to the full theory, and we show that, in the large class of models we are considering, the deformed covariance can not be realized beyond spherical symmetry in the sense that the only deformed theory which leads to a closed constraints algebra is general relativity. Hence, we focus on the spherically symmetric sector, where there exist non-trivial deformed but closed constraints algebras. We investigate the possibility to deform the vectorial constraint as well and we prove that non-trivial deformations of the vectorial constraint with the condition that the constraints algebra remains closed do not exist. Then, we compute the most general deformed Hamiltonian constraint which admits a closed constraints algebra and thus leads to a well-defined effective theory associated with a notion of deformed covariance. Finally, we study static solutions of these effective theories and, remarkably, we solve explicitly and in full generality the corresponding modified Einstein equations, even for the effective theories which do not satisfy the closeness condition. In particular, we give the expressions of the components of the effective metric (for static and spherically symmetric black holes interior) in terms of the functions that govern the deformations of the theory.

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“…Since this point is surrounded by 4-dimensional Euclidean-type space, however, any "bounce" obtained in this way is indeterministic. (It is possible to have holonomy modifications without signature change in models that use self-dual connections [69,70,71] or implement only the Euclidean version of the Hamiltonian constraint [72]. Given the special form of simplified constraints in these models, the genericness of this outcome remains unclear.…”

Section: Modelmentioning

confidence: 99%

Effective Field Theory of Loop Quantum Cosmology

Bojowald

2019

Universe

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Quantum cosmology is traditionally formulated in a minisuperspace setting, implicitly averaging fields over space to obtain homogeneous models. For universal reasons related to the uncertainty principle, quantum corrections then depend on the size of the averaging volume. In minisuperspace truncations, the value of this volume remains an arbitrary parameter devoid of physical meaning, but in an effective field theory it is identified with the infrared scale of inhomogeneous modes. Moreover, the infared scale is running during gravitational collapse, when regions in which homogeneity remains approximately valid shrink to smaller and smaller co-moving sizes. Conceptual implications of this infrared renormalization for perturbative inhomogeneity in quantum cosmology are presented here, mainly for the example of loop quantum cosmology. Several claims made in this framework are altered by infrared

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Covariance in self-dual inhomogeneous models of effective quantum geometry: Spherical symmetry and Gowdy systems

Cited by 27 publications

References 112 publications

Bouncing compact objects. Part I. Quantum extension of the Oppenheimer-Snyder collapse

Bouncing compact objects. Part I. Quantum extension of the Oppenheimer-Snyder collapse

Deformed General Relativity and Quantum Black Holes Interior

Effective Field Theory of Loop Quantum Cosmology

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