Th. Grammenos

Conditional symmetries and the canonical quantization of constrained minisuperspace actions: The Schwarzschild case

Abstract 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 the 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 reparametrization 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”.

Decoupling of the general scalar field mode and the solution space for Bianchi type I and V cosmologies coupled to perfect fluid sources

The scalar field degree of freedom in Einstein’s plus matter field equations is decoupled for Bianchi type I and V general cosmological models. The source, apart from the minimally coupled scalar field with arbitrary potential V(Φ), is provided by a perfect fluid obeying a general equation of state p=p(ρ). The resulting ODE is, by an appropriate choice of final time gauge affiliated to the scalar field, reduced to first order, and then the system is completely integrated for arbitrary choices of the potential and the equation of state.

Moller's energy-momentum complex for a spacetime geometry on a noncommutative curved D3-brane

Abstract Møller’s energy-momentum complex is employed in order to determine the energy and momentum distributions for a spacetime described by a “generalized Schwarzschild” geometry in (3+1)-dimensions on a noncommutative curved D3-brane in an effective, open bosonic string theory. The geometry considered is obtained by an effective theory of gravity coupled with a nonlinear electromagnetic field and depends only on the generalized (effective) mass and charge which incorporate corrections of first order in the noncommutativity parameter.

Energy Distribution in a Schwarzschild-like Spacetime

In this paper, utilizing Møller’s energy-momentum complex, we explicitly evaluate the energy and momentum density associated with a metric describing a four-dimensional, Schwarzschild-like, spacetime derived from an effective gravity coupled with a U(1) gauge field in the context of a D3-brane dynamics in the classical regime, i.e., between the asymptotic and the Planck regime.

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

We use the conditional symmetry approach to study the

Energy Distribution of a Regular Black Hole Solution in Einstein-Nonlinear Electrodynamics

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Locally homogeneous spaces, induced Killing vector fields and applications to Bianchi prototypes

-evolution of a minisuperspace spherically symmetric model both at the classical and quantum level. After integration of the coordinates

Towards canonical quantum gravity for G1 geometries in 2+1 dimensions with a Λ-term

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Canonical quantization of some midi-superspace models in 3+1 dimensions

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Towards canonical quantum gravity for 3+1 geometries admitting maximally symmetric two-dimensional surfaces

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