International Journal of Modern Physics D

We consider general-relativistic rotational perturbations in homogeneous and isotropic Friedmann–Robertson–Walker (FRW) cosmologies. Taking linear perturbations of FRW models, the general solution to the field equations contains tensorial, vectorial and scalar functions. The vectorial terms are in connection with rotations in the given model and due to the Sachs–Wolfe effect they produce contributions to the temperature fluctuations of the cosmic microwave background radiation (CMBR). In this paper we obtain the analytic time dependence of these contributions in a spatially flat FRW model with pressureless ideal fluid, in the presence and the absence of a cosmological constant Λ. We find that the solution can be separated into an integrable and a nonintegrable part, as in the case of scalar perturbations. Analyzing the solutions and using the results of recent observations, we estimate the order of magnitude of the angular velocity corresponding to the rotation tensor at the time of decoupling and today.

The aim of this work is twofold: first, we show how all the n-dimensional Riemannian and Lorentzian metrics can be constructed from a certain class of systems of second-order PDE's which are in duality to the Hamilton–Jacobi equation; second, we impose the Einstein equations on these PDE's.

The evolution of the electric and magnetic components in an effective Yang–Mills condensate dark energy model is investigated. If the electric field is dominant, the magnetic component disappears with the expansion of the Universe. The total YM condensate tracks the radiation in the earlier Universe, and later it becomes w_y ~ -1 and is thus similar to the cosmological constant. So the cosmic coincidence problem can be avoided in this model. However, if the magnetic field is dominant, w_y > 1/3 holds for all time, suggesting that it cannot be a candidate for the dark energy in this case.

In this article, Einstein–Maxwell space–time is considered in connection with some of the astrophysical solutions previously obtained by Tolman (1939) and Bayin (1978). The effect of inclusion of charge in these solutions is investigated thoroughly and the nature of fluid pressure and mass density throughout the sphere is discussed. Mass–radius and mass–charge relations are derived for various cases of the charged matter distribution. Two cases are obtained where perfect fluid with positive pressures gives rise to electromagnetic mass models such that gravitational mass is of purely electromagnetic origin.

This paper deals with the cosmological study of the Bianchi type I model made of dust fluid in the background of dark energy. Cosmological solutions are obtained for the following four cases: (i) only with dark matter; (ii) only with dark energy; (iii) both dark matter and dark energy are present but without interaction; (iv) interactive dark matter and dark energy.

The Bianchi type V magnetized string dust cosmological model for perfect fluid distribution is investigated. We assume that the magnetic field is along the x direction, so F₂₃ is the only nonvanishing component of F_ij. We also find that F₁₄ = 0 = F₂₄ = F₃₄ due to the assumption of infinite electrical conductivity. The behavior of the model in the presence and the absence of a magnetic field is also discussed.

The simplified generalized Chaplygin gas (GCG) model as a candidate of UDME is studied in this paper. By using the latest 162 ESSENCE type Ia supernovae (Sne Ia) data, 30 high red shift Sne Ia data and the distance ratio from z = 0.35 to z = 1089 (the red shift of decoupling), we obtain and at a 95.4% confidence level. In addition the deceleration parameter for this simplified GCG model is investigated, and we find that the universe, at a 1σ confidence level, enters the acceleration era at the red shift z_{q = 0} ~ 0.53 - 0.66 and possesses an acceleration -q_{z = 0} ~ 0.66 - 0.78 at present.

Two phenomenological models of Λ, viz. and , are studied under the assumption that G is a time-variable parameter. Both models show that G is inversely proportional to time, as suggested earlier by others, including Dirac. The models considered here can be matched with observational results by properly tuning the parameters of the models. Our analysis shows that the model corresponds to a repulsive situation and hence correlates with the present status of the accelerating Universe. The other model, , is in general attractive in nature. Moreover, it is seen that due to the combined effect of time-variable Λ and G the Universe evolved with acceleration as well as deceleration. Deceleration indicates a "big crunch".

We find two new classes of exact solutions to the Einstein–Maxwell system of equations. The matter content satisfies a linear equation of state consistent with quark matter; a particular form of one of the gravitational potentials is specified to generate solutions. The exact solutions can be written in terms of elementary functions, and these can be related to quark matter in the presence of an electromagnetic field. The first class of solutions generalizes the Mak–Harko model. The second class of solutions does not admit any singularities in the matter and gravitational potentials at the center.

The motion of test particles along circular orbits in the vacuum C metric is studied in the Frenet–Serret formalism. Special orbits and corresponding intrinsically defined geometrically relevant properties are selectively studied.

Considering both the Gauss–Bonnet and the Born–Infeld terms, which are on a similar footing with regard to the string corrections on the gravity and electrodynamics sides respectively, we present a new class of rotating solutions in Gauss–Bonnet–Born–Infeld gravity with k rotation parameters. Although these solutions are not real in the whole space–time, they can be made real by a suitable transformation. Depending on the metric parameters, these real solutions may be interpreted as black brane solutions with inner and outer event horizons, an extreme black brane or naked singularity. We calculate the finite action and conserved quantities of the solutions by using the counterterm method, and find that these quantities do not depend on the Gauss–Bonnet parameter. We also compute the temperature, the angular velocities, the electric charge and the electric potential. Then, we calculate the entropy of the black brane through the use of the Gibbs–Duhem relation and show that it obeys the area law of entropy. We obtain a Smarr-type formula for the mass as a function of the entropy, the angular momenta and the charge, and show that the conserved and thermodynamic quantities satisfy the first law of thermodynamics. Finally, we perform a stability analysis in both the canonical and the grand-canonical ensemble and show that the presence of a nonlinear electromagnetic field has no effect on the stability of the black branes, which are stable in the whole phase space.

The flat anisotropic model of the early Universe is considered. Two interacting scalar fields with a special form of potential energy are a source of matter fields. Analytic solutions for stages of inflation and preheating are found. It is shown that the solutions tend asymptotically to an isotropic Friedmann model.

We investigate the particle production in a toroidally compactified space–time due to the expansion of a Friedmann cosmological model in ℝ³ × S¹ outside a U(1) local cosmic string. The case of a Friedmann space–time is also investigated where torsion is incorporated in the connection. We present a generalization to toroidal compactification of p extra dimensions, where the topology is given by ℝ³ × T^p. Some implications are presented and discussed. Besides the dynamics of space–time, we investigate in detail the physical consequences of the topological transformations.

Considering a gravitational coupling between the spin and the orbital angular momentum of a spinning test particle orbiting a central massive body, we derive two particular consequences: (1) the influence of the coupling on the location of the innermost stable circular orbit and (2) the gravitomagnetic clock effect due to this coupling. The previous result does not seem to exist for the former, while for the latter we arrive at a result that coincides with what we think is the most accurate.

A time varying space–time metric is shown to be a source of electromagnetic radiation even in the absence of charge sources. The post-Newtonian approximation is used as a realistic model of the connection between the space–time metric and a time-varying gravitational potential. Rapid temporal variations in the metric from the coalescence of relativistic stars are shown to be likely progenitors of gamma ray burst and millisecond pulsars.