International Journal of Modern Physics D

An approximate model of the spacetime foam is offered in which a quantum handle (wormhole) is a 5D wormhole-like solution. Neglecting the linear sizes of the wormhole throat we can introduce a spinor field for an approximate and effective description of the foam. The definition of the spinor field can be made by a dynamic and nondynamic ways. In the first case some field equations are used and the second case leads to superspace. It is shown that the spacetime with the foam is similar to a dielectric with dipoles and supergravity theories with a nonminimal interaction between spinor and electromagnetic fields can be considered as an effective model for the spacetime foam.

The grand unified gauge group G₆≡SU(3)_C ×SU(3)_L× SU(3)_R, which results from compactification of the heterotic superstring onto a three-generation Calabi–Yau space as a maximal subgroup of E₆, contains two superfields, whose scalar components are the conjugates neutrino and the neutral Higgs N, which are singlets of the standard-model gauge group G₄≡SU(3)_C× SU(2)_L×U(1)_Y, and which therefore break G₆to G₄ when they acquire non-vanishing vacuum expectative values. Here, we show how this process can be implemented in two steps when the scalar potential V(ϕ_i) is chosen along a non-D-flat direction, using the "superconducting" model due to Mohapatra and Senjanović, in which one of two scalar fields remains in the asymmetric state up to a temperature T₀~ 10¹⁷GeV, above which the kinetic energy exceeds the potential drop, forcing restoration of the symmetry below the compactification scale T_c ≈ 10¹⁷GeV. This implies that initially, but at low temperatures T ≪ M_w, we find that , thus avoiding the problems associated with large intermediate scales M_I ≳ 10⁹GeV while keeping the Higgs mixing term ~ NH₁H₂ at the right level. A discrete gauge symmetry can prevent the proton from decaying too rapidly.

Concepts like peculiar velocity, gravitational force, and power spectrum and their interrelationships are of utmost importance in the theories of structure formation. The observational implementation of these concepts is usually based on the Newtonian hydrodynamic equations, but used up to scales where general relativistic effects come in. Using a perturbation of FRW metric in harmonic gauge, we show that the relativistic effects reduce to light cone effects including the expansion of the universe.

Within the Newtonian gravitation, the linear perturbation theory of large scale structure formation predicts the peculiar velocity field to be directly proportional to gravitational force due to the matter distribution. The corresponding relation between peculiar velocity field and density contrast has been given by Peebles. Using the general relativistic perturbation we have developed, this familiar relation is modified by doing the calculation on the light cone in contrast to the usual procedure of taking a spacelike slice defined at a definite time. The velocity and density-spectrum are compared to the familiar Newtonian expressions. In particular, the relativistic β-value obtained is reduced and leads to an increased bias factor or a decreased expected amount of the dark matter in a cluster.

We investigate the form of Killing tensors, constructed from conformal Killing vectors of a given spacetime (M, g), by utilizing the Koutras algorithm. As an example we find irreducible Killing tensors in Robertson–Walker spacetimes. A number of theorems are given for the existence of Killing tensors in the conformally related spacetime . The form of the conformally related Killing tensors are explicitly determined. The conditions on the conformal factor Ω relating the two spacetimes (M, g) and are determined for the existence of the tensors. Also we briefly consider the role of recurrent vectors, inheriting conformal vectors and gradient conformal vectors in building Killing tensors.

Conformal collineations (a generalization of conformal motion) and Ricci inheritance collineations, defined by £_ξ R_ab=2α R_ab, for string cloud and string fluids in general relativity are studied. By investigating the kinematical and dynamical properties of such fluids and using the field equations, some recent studies on the restrictions imposed by conformal collineations are extended, and new results are found.

We consider the quasi-classical model of the spin-free configuration on the basis of the self-gravitating spherical dust shell in general relativity. For determination of the energy spectrum of the stationary states on the basis of quasi-classical quantization rules it is required to carry out some regularization of the system. It is realized by an embedding of the initial system in the extended system with rotation. Then, the stationary states of the spherical shells are S-states of the system with the intrinsic momentum. The quasi-classical treatment of a stability of the configuration is associated with the Langer modification of a square of the quantum mechanical intrinsic momentum. It gives value of critical bare mass of the shell determining threshold of stability. For the shell with the bare mass smaller or equal to the Planck's mass, the energy spectra of bound states are found. We obtain the expression for tunneling probability of the shell and construct the quasi-classical model of the pair creation and annihilation of the shells.

Brans–Dicke theory with perfect fluid model has been considered in Bianchi III space–time and exact analytical solutions are presented with barotropic equation of state. These solutions have been analyzed and some of them have shown the properties of inflationary scenario.

In this paper the symmetries of the dual manifold are investigated. We found the conditions when the manifold and its dual admit the same Killing vectors and Killing–Yano tensors. The dual conformal Killing vectors and dual conformal Killing–Yano tensors were investigated. In the case of an Einstein's metric g_μν the corresponding equations for its dual were found. The examples of Kerr–Newman geometry and the separable coordinates in 1+1 dimensions are analyzed in details.

A white dwarf star achieves its equilibrium from the balancing of the gravitational compression against the Fermi degeneracy pressure of the electron gas. In field theory there are examples (e.g. the monopole-charge system) where a strong magnetic field can transform a boson into a fermion or a fermion into a boson. In some condensed matter systems (e.g. fractional quantum Hall systems) a strong magnetic field can transform electrons into effective fermions, or effective anyons. Based on these examples we investigate the possibility that the strong magnetic fields of some white dwarfs may transform some fraction of the electrons into effective bosons. This could have consequences for the structure of highly magnetized white dwarfs. It would alter the mass-radius relationship, and in certain instances one could envision a scenario where a white dwarf below the Chandrasekhar limit could nevertheless collapse into a neutron star due to a weakening of the electron degeneracy pressure. In addition the transformation of electrons into effective bosons could result in the electrons Bose condensing, which could speed up the cooling rate of white dwarfs.

In this paper we have solved the hydrodynamic equations governing the spherically symmetric isothermal accretion (wind) onto (away from) compact objects using various pseudo-Schwarzschild potentials. These solutions are essentially one parameter solutions in a sense that all relevant dynamical as well as thermodynamic quantities for such a flow could be obtained (with the assumption of a one-temperature fluid) if only one flow parameter (temperature of the flow T) is given. Also we have investigated the transonic behaviour of such a flow and showed that for a given T, transitions from subsonic to the supersonic branch of accretion (wind) takes place at different locations depending on the potentials used to study the flow and we have identified these transition zones for flows in various such potentials.

The model of creation of observable particles and particles of the dark matter, considered to be superheavy particles, due to particle creation by the gravitational field of the Friedmann model of the early Universe is given. Estimates on the parameters of the model leading to observable values of the baryon number of the Universe and the dark matter density are made.

We analyze particle production in the spacetime of a chiral cosmic string when it evolves to a static cosmic string configuration. The number of created particles and their energy per unit length of a string are estimated. They appear to be five orders smaller than gravitational particle production in the formation of a static cosmic string but still is rather significant.

We consider the dynamics of a causal bulk viscous cosmological fluid filled flat constantly decelerating Bianchi type I spacetime. The matter component of the Universe is assumed to satisfy a linear barotropic equation of state and the state equation of the small temperature Boltzmann gas. The resulting cosmological models satisfy the condition of smallness of the viscous stress. The time evolution of the relaxation time, temperature, bulk viscosity coefficient and comoving entropy of the dissipative cosmological fluid is also obtained.

In this paper, we study the consequences of the existence of conformal collineations (CC) for string cloud in the context of general relativity. Especially, we interest in special conformal collineation (SCC), generated by a special affine conformal collineation (SACC) in the string cloud. Some results on the restrictions imposed by a conformal collineation symmetry in the string cloud are obtained.