Canonical quantization of the BTZ black hole using Noether symmetries

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

doi:10.1103/physrevd.90.024052

Cited by 28 publications

(39 citation statements)

References 23 publications

(56 reference statements)

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“…Let us now apply the Noether Symmetry Approach [536] (see also [537]) to a general class of f (T ) gravity models where the corresponding Lagrangian of the field equations is given by (641). We start by performing the analysis for arbitrary space-times, and then we focus on static spherically-symmetric geometries.…”

Section: Spherically Symmetric Solutions By Noether Symmetry Approachmentioning

confidence: 99%

f(T) teleparallel gravity and cosmology

et al. 2016

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Over the past decades, the role of torsion in gravity has been extensively investigated along the main direction of bringing gravity closer to its gauge formulation and incorporating spin in a geometric description. Here we review various torsional constructions, from teleparallel, to Einstein-Cartan, and metric-affine gauge theories, resulting in extending torsional gravity in the paradigm of f (T ) gravity, where f (T ) is an arbitrary function of the torsion scalar. Based on this theory, we further review the corresponding cosmological and astrophysical applications. In particular, we study cosmological solutions arising from f (T ) gravity, both at the background and perturbation levels, in different eras along the cosmic expansion. The f (T ) gravity construction can provide a theoretical interpretation of the late-time universe acceleration, alternative to a cosmological constant, and it can easily accommodate with the regular thermal expanding history including the radiation and cold dark matter dominated phases. Furthermore, if one traces back to very early times, for a certain class of f (T ) models, a sufficiently long period of inflation can be achieved and hence can be investigated by cosmic microwave background observations, or alternatively, the Big Bang singularity can be avoided at even earlier moments due to the appearance of non-singular bounces. Various observational constraints, especially the bounds coming from the large-scale structure data in the case of f (T ) cosmology, as well as the behavior of gravitational waves, are described in detail. Moreover, the spherically symmetric and black hole solutions of the theory are reviewed. Additionally, we discuss various extensions of the f (T ) paradigm. Finally, we consider the relation with other modified gravitational theories, such as those based on curvature, like f (R) gravity, trying to enlighten the subject of which formulation, or combination of formulations, might be more suitable for quantization ventures and cosmological applications. Contents

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Section: Spherically Symmetric Solutions By Noether Symmetry Approachmentioning

confidence: 99%

f(T) teleparallel gravity and cosmology

et al. 2016

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“…In order to reduce the number of the free parameters we apply the initial condition a (t → 0) ≃ 0 + , which gives that x 0 ≃ y 0 . Moreover in the de Sitter points, in which the Ricciscalar is given by the expressions (48) and (49), we observe that if we set, β ≃ H 2 0 , βV 1 ≃ H 2 0 , and βV 2 ≃ H 0 , then R 0 ≃ H 2 0 . As we discussed the value of the conservation law I 5 can be related with the energy density of the radiation fluid which is introduced by the theory, in the present era Ω r is small, that is, we can assume that I 5 ≃ 0.…”

Section: Fv (R)-modelmentioning

confidence: 73%

“…On the other hand, Noether point symmetries have been introduced as a selection rule for the determination of the functional form of the potential in scalar field cosmology in [40]. Since then that method has been applied in various cosmological models and new solutions have been found (for instance see [41][42][43][44][45][46][47][48][49][50] and references cited therein). In [51] Noether symmetries were applied in the scalar field cosmological scenario as a geometric selection rule for the determination of the functional form of the potential.…”

Section: Introductionmentioning

confidence: 99%

f ( R )-gravity from Killing tensors

Paliathanasis

2016

Class. Quantum Grav.

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We consider f (R)-gravity in a Friedmann-Lemaître-Robertson-Walker spacetime with zero spatial curvature. We apply the Killing tensors of the minisuperspace in order to specify the functional form of f (R) and the field equations to be invariant under Lie-Bäcklund transformations which are linear in the momentum (contact symmetries). Consequently, the field equations to admit quadratic conservation laws given by Noether's Theorem. We find three new integrable f (R) models, for which with the application of the conservation laws we reduce the field equations to a system of two firstorder ordinary differential equations. For each model we study the evolution of the cosmological fluid. Where we find that for the one integrable model the cosmological fluid has an equation of state parameter, in which in the latter there is a linear behavior in terms of the scale factor which describes the Chevallier, Polarski and Linder (CPL) parametric dark energy model. 95.35.+d, 95.36.+x

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“…Since the quantum potentials do not vanish, it is expected that the semiclassical spacetime will differ from the classical. Following the usual steps for finding the semiclassical solution, we find that the final line element is 40) in which remain three essential constants after performing allowed coordinate transformations. The Ricci scalar becomes infinite for T → 0 as well as for T → ∞ for negative values of λ 3 parameter, while it vanishes at this limit for positive values of this parameter.…”

Section: Subalgebramentioning

confidence: 99%

Conditional symmetries in axisymmetric quantum cosmologies with scalar fields and the fate of the classical singularities

Zampeli

Pailas

Terzis

et al. 2016

J. Cosmol. Astropart. Phys.

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Abstract. In this paper, the classical and quantum solutions of some axisymmetric cosmologies coupled to a massless scalar field are studied in the context of minisuperspace approximation. In these models, the singular nature of the Lagrangians entails a search for possible conditional symmetries. These have been proven to be the simultaneous conformal symmetries of the supermetric and the superpotential. The quantization is performed by adopting the Dirac proposal for constrained systems, i.e. promoting the first-class constraints to operators annihilating the wave function. To further enrich the approach, we follow [1] and impose the operators related to the classical conditional symmetries on the wave function. These additional equations select particular solutions of the Wheeler-DeWitt equation. In order to gain some physical insight from the quantization of these cosmological systems, we perform a semiclassical analysis following the Bohmian approach to quantum theory. The generic result is that, in all but one model, one can find appropriate ranges of the parameters, so that the emerging semiclassical geometries are non-singular. An attempt for physical interpretation involves the study of the effective energy-momentum tensor which corresponds to an imperfect fluid.

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Canonical quantization of the BTZ black hole using Noether symmetries

Cited by 28 publications

References 23 publications

f(T) teleparallel gravity and cosmology

f(T) teleparallel gravity and cosmology

f ( R )-gravity from Killing tensors

Conditional symmetries in axisymmetric quantum cosmologies with scalar fields and the fate of the classical singularities

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