LARGE-SCALE PATHOLOGY OF UNIVERSES WITH VII0×VIII ISOMETRIES

The goal of this paper is to show somewhat unexpected globally pathologic properties in universes described by a class of static planary symmetric exact solutions with G ₆-group of motion. In order to achieve this aim, the Killing vectors, the null geodesics and the Penrose diagrams corresponding to different expressions of g ₄₄=–e ^2f(z), with f(z) solutions of Einstein's equations, have been employed. Finally, woking in a particular gauge, we focus on the behaviour of the radiating electromagnetic modes and derive the observable components of E and B and the expressions of the essential component of the Umov-Poynting vector.     

A Maxwell Field Equations Class of Exact Solutions on Matter-Dominated Spatially Closed Friedman-Robertson-Walker Universe

Working in a spatially closed Friedman-Robertson-Walker universe with cosmological dust, we investigate a particular source-free Maxwell field generated by a rotationally-symmetric potential A with one of the components in the direction of and the other along . Using the (, , )-Euler coordinates on S ³ and a compact timelike coordinate f, we obtain a class of parametric solutions that allows us to write down the essential components of the Maxwell tensor as well as the induction and the electric field intensity pointing out, besides the non-propagating fundamental electric field, a burst of electromagnetic radiation.     

Spatially-Hyperbolic Friedmann–Robertson–Walker Universe with Potentially Broken Z2−Symmetry

For the Friedmann–Robertson–Walker (FRW) Universe with negative curvature, sustained by a spontaneous Z₂? symmetry breaking scalar field, depending on time alone, we have derived the Einstein–Gordon system of equations. For physically relevant cases, the matter-curvature system have been numerically analyzed.     

Fermions in a Kerr-Newman space-time

The aim of this paper is to put the U(1) -gauge theory of fermions in the spacetime described by a Kerr-Newman metric. The field equations have rather complicated expressions essentially different from the Minkowskian spacetime.     

The <Emphasis Type="Italic">A</Emphasis><Emphasis Type="Italic">d</Emphasis><Emphasis Type="Italic">S</Emphasis><Subscript>5</Subscript> Warp of Spatially Hyperbolic Universes,Spinless Modes and Spectra and the Corresponding Wheeler–DeWitt Schrödinger-Like Equation

In this paper, we consider an A d S ₅ bulk with k=?1? FRW branes, together with bosons test particles, evolving in the 5D hyperspace. In the first part, we compute the wave function of the scalar fields in the bulk and the allowed mass spectrum for physically relevant cases. Also, an important quantization law, connecting the mass spectrum of the bosons on the brane and the bulk mass parameter is written down. In the second part, in oder to develop a quantization model, we use the Wheeler-DeWitt equation and solve its Schrödinger-like form, obtaining the wave function of the Universe. The solutions describe a universe emerging out of nothing, without tunneling. Lastly, using a mixture of states, we emphasize a smooth universe, with neither Bangs nor Crunches.     

The Quantum Treatment of the 5D-Warped Friedmann–Robertson–Walker Universe in Schrödinger Picture

The present paper is devoted to the time-evolving Schrödinger version of the Wheeler–De Witt equation, written for the five dimensional warped k=0—FRW Universe. For small values of the cosmological scale factor, a, the wave function of the Universe is expressed in terms of the Heun Double Confluent functions, which have been intensively worked out in the last years. As expected, for large a’s, one gets the well-known Hermite associated functions. Within the semiclassical approximation, valid for large n, the asymptotic representation of the Whittaker functions leads to the “free particle” behavior.     

Planary symmetric static worlds with massless scalar sources

Motivated by the recent wave of investigations on plane domain wall spacetimes with nontrivial topologies, the present paper deals with (probably) the most simple source field configuration which can generate a spatially planary symmetric static spacetime, namely a minimally coupled massless scalar field that depends only upon a spacelike coordinate. z. It is shown that the corresponding exact solutions (. g_±) are algebraically special, type D-[S-3T] (in11), and represent globally pathologic spacetimes with a G₄-group of motion acting on R² × R orbits. In spite of the model simplicity, these -generated worlds possess naked timelike singularities (reached within a finite universal time by normal nonspacelike geodesics). are completely free of Cauchy surfaces, and contain, in the t-leveled sections, points that cannot be joined by C¹-trajectory images of oblique non-spacelike geodesies. Finally, we comment on the possibility of deriving from (, g_±) two other physically interesting -generated spacetimes by appropriate joining conditions in the (z=0)-plane.Monbusho fellow, on leave of absence from Al. I. Cuza University of lasi. Romania).     

U(1) gauge theory of the quantum hall effect

The solution of the Klein-Gordon equation for a complex scalar field in the presence of an electrostatic field orthogonal to a magnetostatic field is analyzed. Considerations concerning the quantum Hall-type evolution are presented also. Using the Hamiltonian with a self-interaction term, we obtain a critical value for the magnetic field in the case of the spontaneous symmetry breaking.