Lie point and variational symmetries in minisuperspace Einstein gravity

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

doi:10.1088/1751-8113/47/9/095202

Cited by 110 publications

(130 citation statements)

References 33 publications

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“…However, these are not the only existing integrals of motion. As shown in [21], in principle, all conformal Killing vectors of the supermetric define rheonomic integrals of motion. For example, the relation £ ξ G µν = ω G µν implies that if we define the phase-space quantity Q ξ = ξ µ p µ , then…”

Section: Classical Formulation and Conditional Symmetriesmentioning

confidence: 97%

Minisuperspace canonical quantization of the Reissner-Nordström black hole via conditional symmetries

et al. 2014

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We use the conditional symmetry approach to study the r-evolution of a minisuperspace spherically symmetric model both at the classical and quantum level. After integration of the coordinates t, θ and φ in the gravitational plus electromagnetic action the configuration space dependent dynamical variables turn out to correspond to the r-dependent metric functions and the electrostatic field. In the context of the formalism for constrained systems (Dirac -Bergmann, ADM) with respect to the radial coordinate r, we set up a point-like reparameterization invariant Lagrangian. It is seen that, in the constant potential parametrization of the lapse, the corresponding minisuperspace is a Lorentzian three-dimensional flat manifold which obviously admits six Killing vector fields plus a homothetic one. The weakly vanishing r-Hamiltonian guarantees that the phase space quantities associated to the six Killing fields are linear holonomic integrals of motion. The homothetic field provides one more rheonomic integral of motion. These seven integrals are shown to comprise the entire classical solution space, i.e. the space-time of a Reissner-Nordström black hole, the rreparametrization invariance since one dependent variable remains unfixed, and the two quadratic relations satisfied by the integration constants. We then quantize the model using the quantum analogues of the classical conditional symmetries, and show that the existence of such symmetries yields solutions to the Wheeler-DeWitt equation which, as a semiclassical analysis shows, exhibit a good correlation with the classical regime. We use the resulting wave functions to investigate the possibility of removing the classical singularities.

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Section: Classical Formulation and Conditional Symmetriesmentioning

confidence: 97%

Minisuperspace canonical quantization of the Reissner-Nordström black hole via conditional symmetries

et al. 2014

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“…However, as it can be seen, the field equations in the space of variables {N, a, φ} form a singular dynamical system with constraint equation ∂L ∂N = 0. Hence, using [44] with the application of the results of [45], it has been shown that the gravitational field equations which follow from (18) admit an infinite number of (nonlocal) conservation laws. Specifically, every conformal Killing vector of the minisuperspace {a, φ} provides a conservation law and, as the minisuperspace has dimension two, the dimension of the conformal algebra is infinite and consequently we have an infinite number of conservation laws.…”

Section: General Analytical Solutionmentioning

confidence: 99%

“…Here, it is important to note that these conservation laws are not necessarily in involution. For more details see [45].…”

Section: General Analytical Solutionmentioning

confidence: 99%

Observational constraints on new exact inflationary scalar-field solutions

Barrow

Paliathanasis

2016

Phys. Rev. D

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An algorithm is used to generate new solutions of the scalar field equations in homogeneous and isotropic universes. Solutions can be found for pure scalar fields with various potentials in the absence and presence of spatial curvature and other perfect fluids. A series of generalisations of the Chaplygin gas and bulk viscous cosmological solutions for inflationary universes are found. Furthermore other closed-form solutions which provide inflationary universes are presented. We also show how the Hubble slow-roll parameters can be calculated using the solution algorithm and we compare these inflationary solutions with the observational data provided by the Planck 2015 collaboration in order to constraint and rule out some of these models.PACS numbers: 98.80.-k, 95.35.+d, 95.36.+x

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“…[1,[21][22][23][24][25]). In [26], the relation between the Lie point symmetries and the conditional symmetries of the minisuperspace was established which in the constant potential lapse parametrization coincide with the conditional symmetries in the phase space. A different approach regarding the Lie point symmetries and the gauge fixing of the lapse function was taken in [27,28] and applied in [29][30][31].…”

Section: General Considerationsmentioning

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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Lie point and variational symmetries in minisuperspace Einstein gravity

Cited by 110 publications

References 33 publications

Minisuperspace canonical quantization of the Reissner-Nordström black hole via conditional symmetries

Minisuperspace canonical quantization of the Reissner-Nordström black hole via conditional symmetries

Observational constraints on new exact inflationary scalar-field solutions

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

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