Contact symmetries of constrained systems and the associated integrals of motion

Dimakis, N.; Terzis, Petros A.; Christodoulakis, T.

doi:10.1088/1742-6596/633/1/012040

Cited by 7 publications

(8 citation statements)

References 16 publications

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“…In the context of symmetry-reduced models, it has recently been shown that homogeneous and isotropic cosmology coupled with a massless scalar field exhibits a 1-dimensional SL(2, ) conformal invariance in the form of Möbius transformations of the proper time [37][38][39][40][41] (see also [42][43][44][45][46]). This symmetry also exists in Bianchi I models [38] and in the presence of a cosmological constant [41], and the relationship with this latter was in fact already pointed out by Gibbons in [47].…”

Section: Introductionmentioning

confidence: 99%

Symmetries of the black hole interior and singularity regularization

2021

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We reveal an \mathfrak{iso}(2,1)𝔦𝔰𝔬(2,1) Poincar'e algebra of conserved charges associated with the dynamics of the interior of black holes. The action of these Noether charges integrates to a symmetry of the gravitational system under the Poincar'e group ISO(2,1)(2,1), which allows to describe the evolution of the geometry inside the black hole in terms of geodesics and horocycles of AdS{}_22. At the Lagrangian level, this symmetry corresponds to M"obius transformations of the proper time together with translations. Remarkably, this is a physical symmetry changing the state of the system, which also naturally forms a subgroup of the much larger \textrm{BMS}_{3}=\textrm{Diff}(S^1)\ltimes\textrm{Vect}(S^1)BMS3=Diff(S1)⋉Vect(S1) group, where S^1S1 is the compactified time axis. It is intriguing to discover this structure for the black hole interior, and this hints at a fundamental role of BMS symmetry for black hole physics. The existence of this symmetry provides a powerful criterion to discriminate between different regularization and quantization schemes. Following loop quantum cosmology, we identify a regularized set of variables and Hamiltonian for the black hole interior, which allows to resolve the singularity in a black-to-white hole transition while preserving the Poincar'e symmetry on phase space. This unravels new aspects of symmetry for black holes, and opens the way towards a rigorous group quantization of the interior.

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Section: Introductionmentioning

confidence: 99%

Symmetries of the black hole interior and singularity regularization

2021

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“…In the context of symmetry-reduced models, it has recently been shown that homogeneous and isotropic cosmology coupled with a massless scalar field exhibits a 1-dimensional SL(2, R) conformal invariance in the form of Möbius transformations of the proper time [37][38][39][40][41] (see also [42][43][44][45][46]). This symmetry also exists in Bianchi I models [38] and in the presence of a cosmological constant [41], and the relationship with this latter was in fact already pointed out by Gibbons in [47].…”

Section: Introductionmentioning

confidence: 99%

Symmetries of the Black Hole Interior and Singularity Regularization

Geiller,

Livine,

Sartini

2020

Preprint

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We reveal an iso(2, 1) Poincaré algebra of conserved charges associated with the dynamics of the interior of black holes. The action of these Noether charges integrates to a symmetry of the gravitational system under the Poincaré group ISO(2, 1), which allows to describe the evolution of the geometry inside the black hole in terms of geodesics and horocycles of AdS 2 . At the Lagrangian level, this symmetry corresponds to Möbius transformations of the proper time together with translations. Remarkably, this is a physical symmetry changing the state of the system, which also naturally forms a subgroup of the much larger BMS 3 = Diff(S 1 ) ⋉ Vect(S 1 ) group, where S 1 is the compactified time axis. It is intriguing to discover this structure for the black hole interior, and this hints at a fundamental role of BMS symmetry for black hole physics. The existence of this symmetry provides a powerful criterion to discriminate between different regularization and quantization schemes. Following loop quantum cosmology, we identify a regularized set of variables and Hamiltonian for the black hole interior, which allows to resolve the singularity in a black-to-white hole transition while preserving the Poincaré symmetry on phase space. This unravels new aspects of symmetry for black holes, and opens the way towards a rigorous group quantization of the interior.

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“…The authors [56][57][58][59][60][61][62] have also studied the phase space symmetries of homogeneous cosmological models (without explicit reference to an sl(2, R) CVH algebra however), but using a field space formulation. This formulation is based on the following simple observation: When evaluating the Einstein-Hilbert action on a minisuperspace line element, the action reduces to a one-dimensional mechanical model of the form…”

Section: Introductionmentioning

confidence: 99%

Dynamical symmetries of homogeneous minisuperspace models

Geiller,

Livine,

Sartini

2022

Preprint

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We investigate the phase space symmetries and conserved charges of homogeneous gravitational minisuperspaces. These (0 + 1)-dimensional reductions of general relativity are defined by spacetime metrics in which the dynamical variables depend only on a time coordinate, and are formulated as mechanical systems with a non-trivial field space metric (or supermetric) and effective potential. We show how to extract conserved charges for those minisuperspaces from the homothetic Killing vectors of the field space metric. In the case of two-dimensional field spaces, we exhibit a universal 8-dimensional symmetry algebra A = sl(2, R) ⊕ R + h 2 , based on the two-dimensional Heisenberg algebra h 2 ≃ R 4 . We apply this to the systematic study of the Bianchi models for homogeneous cosmology. This extends previous results on the sl(2, R) CVH algebra for FLRW cosmology, and the Poincaré symmetry for Kantowski-Sachs metrics describing the black hole interior. The presence of this rich symmetry structure already in minisuperspace models opens new doors towards quantization and the study of solution generating mechanisms.

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Contact symmetries of constrained systems and the associated integrals of motion

Abstract: View the article online for updates and enhancements.

Cited by 7 publications

References 16 publications

Symmetries of the black hole interior and singularity regularization

Symmetries of the black hole interior and singularity regularization

Symmetries of the Black Hole Interior and Singularity Regularization

Dynamical symmetries of homogeneous minisuperspace models

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