arXiv subjects

N. Dimakis

Publications and source records attributed to N. Dimakis.

43 records · Page 3Linked to original sources

arXiv2014

Noether analysis of Scalar-Tensor Cosmology

A scalar--tensor theory of gravity, containing an arbitrary coupling function $F(ϕ)$ and a general potential $V(ϕ)$, is considered in the context of a spatially flat FLRW model. The use of reparametrization invariance enables a particular lapse parametrization in which the mini--superspace metric completely specifies the dynamics of the system. A requirement of existence of the maximal possible number of autonomous integrals of motion is imposed. This leads to a flat mini--superspace metric realized by a particular relation between the coupling function and the potential. The space of solutions is completely described in terms of the three autonomous integrals of motion constructed by the Killing fields of the mini--supermetric and an additional rheonomous emanating from the homothetic field. The solutions contain the arbitrary function which remains after the imposition of the relation between $F(ϕ)$ and $V(ϕ)$. To exemplify the use of the general results, we select some particular cases and study their physical implications through an effective energy--momentum tensor, which tends out to be that of a perfect fluid.

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arXiv2014

Canonical Quantization of the BTZ Black Hole using Noether Symmetries

The well-known BTZ black hole solution of (2+1) Einstein's gravity, in the presence of a cosmological constant, is treated both at the classical and quantum level. Classically, the imposition of the two manifest local Killing fields of the BTZ geometry at the level of the full action results in a mini-superspace constraint action with the radial coordinate playing the role of the independent dynamical variable. The Noether symmetries of this reduced action are then shown to completely determine the classical solution space, without any further need to solve the dynamical equations of motion. At a quantum mechanical level, all the admissible sets of the quantum counterparts of the generators of the above mentioned symmetries are utilized as supplementary conditions acting on the wave-function. These additional restrictions, in conjunction with the Wheeler-DeWitt equation, help to determine (up to constants) the wave-function which is then treated semiclassically, in the sense of Bohm. The ensuing space-times are, either identical to the classical geometry, thus exhibiting a good correlation of the corresponding quantization to the classical theory, or are less symmetric but exhibit no Killing or event horizon and no curvature singularity, thus indicating a softening of the classical conical singularity of the BTZ geometry.

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arXiv2013

FLRW metric $f(R)$ cosmology with a perfect fluid by generating integrals of motion

In the context of metric f(R) gravity, we consider a FLRW space-time, filled with a perfect fluid described by a barotropic equation of state (p = γρ). We give the equivalent mini-superspace description and use the reparametrization invariance of the resulting Lagrangian to work in the equivalent constant potential description. At that point, we restrict our analysis to those models for which the ensuing scaled mini-superspace is maximally symmetric. Those models exhibit the maximum number of autonomous integrals of motion linear in the momenta, which are constructed by the Killing vectors of the respective mini-supermetric. The integrals of motion are used to analytically solve the equations of the corresponding models. Finally, a brief description of the properties of the resulting Hubble parameters is given.

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arXiv2013

Minisuperspace Canonical Quantization of the Reissner-Nordstrom Black Hole via Conditional Symmetries

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 $r$-reparametrization 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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arXiv2013

Lie - point and variational symmetries in minisuperspace Einstein's gravity

We consider the application of the theory of symmetries of coupled ordinary differential equations to the case of reparametrisation invariant Lagrangians quadratic in the velocities; such Lagrangians encompass all minisuperspace models. We find that, in order to acquire the maximum number of symmetry generators, one must (a) consider the lapse $N(t)$ among the degrees of freedom and (b) allow the action of the generator on the Lagrangian and/or the equations of motion to produce a multiple of the constraint, rather than strictly zero. The result of this necessary modification of the standard theory (concerning regular systems) is that the Lie - point symmetries of the equations of motion are exactly the variational symmetries (containing the time reparametrisation symmetry) plus the well known scaling symmetry. These variational symmetries are seen to be the simultaneous conformal Killing fields of both the metric and the potential, thus coinciding with the conditional symmetries defined in phase space. In a parametrisation of the lapse for which the potential becomes constant, the generators of the aforementioned symmetries become the Killing fields of the scaled supermetric and the homothetic field respectively.

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arXiv2012

Conditional Symmetries and the Canonical Quantization of Constrained Minisuperspace Actions: the Schwarzschild case

A conditional symmetry is defined, in the phase-space of a quadratic in velocities constrained action, as a simultaneous conformal symmetry of the supermetric and the superpotential. It is proven that such a symmetry corresponds to a variational (Noether) symmetry.The use of these symmetries as quantum conditions on the wave-function entails a kind of selection rule. As an example, the minisuperspace model ensuing from a reduction of the Einstein - Hilbert action by considering static, spherically symmetric configurations and r as the independent dynamical variable, is canonically quantized. The conditional symmetries of this reduced action are used as supplementary conditions on the wave function. Their integrability conditions dictate, at a first stage, that only one of the three existing symmetries can be consistently imposed. At a second stage one is led to the unique Casimir invariant, which is the product of the remaining two, as the only possible second condition on $Ψ$. The uniqueness of the dynamical evolution implies the need to identify this quadratic integral of motion to the reparametrisation generator. This can be achieved by fixing a suitable parametrization of the r-lapse function, exploiting the freedom to arbitrarily rescale it. In this particular parametrization the measure is chosen to be the determinant of the supermetric. The solutions to the combined Wheeler - DeWitt and linear conditional symmetry equations are found and seen to depend on the product of the two "scale factors"

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arXiv2011

Classical and Quantum Bianchi Type III vacuum Horava - Lifshitz Cosmology

A diagonal Bianchi Type III space-time is treated, both at the classical and quantum level, in the context of Horava - Lifshitz gravity. The system of the classical equations of motion is reduced to one independent Abel's equation of the first kind. Closed form solution are presented for various values of the coupling constants appearing in the action. Due to the method used, solutions of Euclidean, Lorentzian and neutral signature are attained. The solutions corresponding to \lamda <> 1 are seen to develop curvature singularities as the other constants approach their Einsteinian values, in contrast to those with \lamda = 1 which tend to the known Einstein gravity solutions. At the quantum level, the resulting Wheeler-DeWitt equation is explicitly solved for \lamda = 1, σ= 0 and \lamda = 1/3 . The ensuing wave-functions diverge in the Einsteinian limit.

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