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(Phi), is provided by a perfect fluid obeying a general equation of state p =p(rho). The resulting ODE is, by an appropriate choice of final time gauge affiliated to the scalar field, reduced to 1st order, and then the system is completely integrated for arbitrary choices of the potential and the equation of state.Comment: latex2e source file,14 pages, no figures; (v3): minor corrections, to appear in J. Math. Phy

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.Comment: 24 pages, no figures, LaTeX 2e source fil

A Non - Singular Cosmological Model with Shear and Rotation

We have investigated a non-static and rotating model of the universe with an imperfect fluid distribution. It is found that the model is free from singularity and represents an ever expanding universe with shear and rotation vanishing for large value of time.Comment: 10 pages, late

Optimal privatization portfolios in the presence of arbitrary risk aversion

We consider the global portfolio of privatized state assets from 1985 to 2012 in the non-parametric decision-making context of Stochastic Dominance Efficiency for broad classes of investor preferences. We estimate all possible portfolios in the context of Strategic vs. non-Strategic and Cyclical vs. non-Cyclical asset allocations that dominate the market benchmark and provide a complete efficiency ranking. The optimal solutions are computed using linear and mixed integer programming formulations. Dominant portfolios tend to overweight non-Cyclical and non-Strategic assets, while rotation may take place across business cycles. Bayesian investment style return attribution analysis, based on Monte Carlo Integration, suggests that Growth drives returns during the first business cycle, rotating to a balanced mix of styles with Size and Debt Leverage during the second business cycle and finally to Size during the last business cycle. Value is found to be the least influential style in all periods

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 $\Psi$. 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"Comment: 20 pages, LaTeX2e source file, no figure

Towards Canonical Quantum Gravity for G1 Geometries in 2+1 Dimensions with a Lambda--Term

The canonical analysis and subsequent quantization of the (2+1)-dimensional action of pure gravity plus a cosmological constant term is considered, under the assumption of the existence of one spacelike Killing vector field. The proper imposition of the quantum analogues of the two linear (momentum) constraints reduces an initial collection of state vectors, consisting of all smooth functionals of the components (and/or their derivatives) of the spatial metric, to particular scalar smooth functionals. The demand that the midi-superspace metric (inferred from the kinetic part of the quadratic (Hamiltonian) constraint) must define on the space of these states an induced metric whose components are given in terms of the same states, which is made possible through an appropriate re-normalization assumption, severely reduces the possible state vectors to three unique (up to general coordinate transformations) smooth scalar functionals. The quantum analogue of the Hamiltonian constraint produces a Wheeler-DeWitt equation based on this reduced manifold of states, which is completely integrated.Comment: Latex 2e source file, 25 pages, no figures, final version (accepted in CQG

Bianchi type II,III and V diagonal Einstein metrics re-visited

We present, for both minkowskian and euclidean signatures, short derivations of the diagonal Einstein metrics for Bianchi type II, III and V. For the first two cases we show the integrability of the geodesic flow while for the third case a somewhat unusual bifurcation phenomenon takes place: for minkowskian signature elliptic functions are essential in the metric while for euclidean signature only elementary functions appear