Narrow Results

We calculate the vacuum averages of the energy–momentum tensor associated with a massless left-handed spinor fields due to magnetic fluxes on idealized cosmic string spacetime. In this analysis three distinct configurations of magnetic fields are considered: (i) a homogeneous field inside the tube, (ii) a magnetic field proportional to 1/r, and (iii) a cylindrical shell with δ-function. In these three cases the axis of the infinitely long tubes of radius R coincides with the cosmic string. In order to proceed with these calculations we explicitly obtain the Euclidean Feynman propagators associated with these physical systems. As we shall see, these propagators possess two distinct parts. The first are the standard ones, i.e. corresponding to the spinor Green's functions associated with the massless fermionic fields on the idealized cosmic string spacetime with a magnetic flux running through the line singularity. The second parts are new, they are due to the finite thickness of the radius of the tubes. As we shall see these extra parts provide relevant contributions to the vacuum averages of the energy–momentum tensor.

We have investigated the bulk viscous fluid string dust cosmological model in the higher dimensional space–time. To obtain a determinate solution, it is assumed that the coefficient of bulk viscosity is a power function of the energy density τ = τ_cρ^m(t) and the scalar of expansion is proportional to shear scalar, which leads to a relation between metric potentials A = KRⁿ where A and R are functions of time. It is also observed that models appear to be singular at and in the presence and absence of bulk viscosity and for n = 1, the model represent an isotropic universe. The physical and geometrical aspects of the model are also discussed.

We consider a nonlinear sigma model coupled to the metric of a conic space. We obtain restrictions for a nonlinear sigma model to be a source of the conic space. We then study a nonlinear sigma model in the conic space background. We find coordinate transformations which reduce the chiral fields equations in the conic space background to field equations in Minkowski space–time. This enables us to apply the same methods for obtaining exact solutions in Minkowski space–time to the case of a conic space–time. In the case the solutions depend on two spatial coordinates we employ Ivanov's geometrical ansatz. We give a general analysis and also present classes of solutions in which there is dependence on three and four coordinates. We discuss with special attention the intermediate, instanton and meron solutions and their analogous in the conic space. We find differences in the total actions and topological charges of these solutions and discuss the role of the deficit angle.

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.

Exact solutions to the Einstein field equations with cosmic string and a space-varying cosmological constant, viz. Λ = Λ(r), in the energy–momentum tensors are presented. Three cases have been studied: the variable cosmological constant (1) has power law dependence, (2) is proportional to the string fluid density, and (3) is purely a constant. Some cases of interesting physical consequences have been found where (i) the variable cosmological constant can be represented by a power law of the type Λ = 3r^-2, (ii) the variable cosmological constant and the cosmic string density are interdependent according to the relation Λ = -8πρ_s, and (iii) the cosmic string density can be scaled by a power law of the type ρ_s = r^-2. It is also shown that several known solutions can be recovered from the general form of the solutions obtained here.

In this paper, we analyze the bosonic current densities induced by a magnetic flux running along an idealized cosmic string in a high-dimensional spacetime, admitting that the coordinate along the string's axis is compactified. Additionally we admit the presence of a magnetic flux enclosed by the compactification axis. In order to develop this analysis we calculate the complete set of normalized bosonic wave functions obeying a quasiperiodicity condition, with arbitrary phase β, along the compactified dimension. In this context, only azimuthal and axial currents densities take place. As to the azimuthal current, two contributions appear. The first contribution corresponds to the standard azimuthal current in a cosmic string spacetime without compactification, while the second contribution is a new one, induced by the compactification itself. The latter is an even function of the magnetic flux enclosed by the string axis and is an odd function of the magnetic flux along its core with period equal to quantum flux, Φ₀ = 2π/e. On the other hand, the nonzero axial current density is an even function of the magnetic flux along the core of the string and an odd function of the magnetic flux enclosed by it. We also find that the axial current density vanishes for untwisted and twisted bosonic fields in the absence of the magnetic flux enclosed by the string axis. Some asymptotic expressions for the current density are provided for specific limiting cases of the physical parameter of the model.

We consider the Casimir effect, by calculating the Casimir energy and its corrections for nonzero temperatures, of a massless scalar field in the spacetime with topology $S^3\times R^1$ (Einstein universe) containing an idealized cosmic string. The obtained results confirm the role played by the identifications imposed on the quantum field by boundary conditions arising from the topology of the gravitational field under consideration and illustrate a realization of a gravitational analogue of the Casimir effect. In this backgorund, we show that the vacuum energy can be written as a term which corresponds to the vacuum energy of the massless scalar field in the Einstein universe added by another term that formally corresponds to the vacuum energy of the electromagnetic field in the Einstein universe, multiplied by a parameter associated with the presence of the cosmic string, namely, $\lambda =(1/\alpha )-1$, where $\alpha$ is a constant related to the cosmic string tension, $G\mu$.

We investigate combined effects of nontrivial topology, induced by a cosmic string, and boundaries on the fermionic condensate and the vacuum expectation value (VEV) of the energy–momentum tensor for a massive fermionic field. As geometry of boundaries we consider two plates perpendicular to the string axis on which the field is constrained by the MIT bag boundary condition. By using the Abel–Plana type summation formula, the VEVs in the region between the plates are decomposed into the boundary-free and boundary-induced contributions for general case of the planar angle deficit. The boundary-induced parts in both the fermionic condensate and the energy–momentum tensor vanish on the cosmic string. Fermionic condensate is positive near the string and negative at large distances, whereas the vacuum energy density is negative everywhere. The radial stress is equal to the energy density. For a massless field, the boundary-induced contribution in the VEV of the energy–momentum tensor is different from zero in the region between the plates only and it does not depend on the coordinate along the string axis. In the region between the plates and at large distances from the string, the decay of the topological part is exponential for both massive and massless fields. This behavior is in contrast to that for the VEV of the energy–momentum tensor in the boundary-free geometry with the power law decay for a massless field. The vacuum pressure on the plates is inhomogeneous and vanishes at the location of the string. The corresponding Casimir forces are attractive.

Dynamical evolution of the cosmic string in a spherically symmetric $f(R)$ gravity vacuum is studied for a closed and straight string. We first set the background spacetime metric for a constant curvature scalar $R=R_0$, and obtain the Killing fields for it. Using the standard gauge coordinates and constraints for both closed and straight strings, we present the equation of motions and find the solutions of them. We then analyze the dynamics of the string by studying the behavior of the string radius and periastron radius, with respect to both proper time and azimuthal angle, for various values of $f(R)$ functions. Consequently, we conclude that the value of $f(R)$ dramatically affects the closed string collapse time and the straight string angular deviation.

In this paper we present a complete and detailed analysis of the calculation of both the Wightman function and the vacuum expectation value of the energy–momentum tensor that arise from quantum vacuum fluctuations of massive and massless scalar fields in the cosmic dispiration spacetime, which is formed by the combination of two topological defects: a cosmic string and a screw dislocation. This spacetime is obtained in the framework of the Einstein–Cartan theory of gravity and is considered to be a chiral spacelike cosmic string. For completeness we perform the calculation in a high-dimensional spacetime, with flat extra dimensions. We found closed expressions for the energy–momentum tensor and, in particular, in $(3+1)$-dimensions, we compare our results with previous existing ones in the literature for the massless scalar field case.

We have studied LRS Bianchi type I cosmological models with barotropic perfect fluid and cosmic string in the framework of $f(T)$ theory of gravitation. We have assumed that expansion of the model is proportional to the shear scalar. Hybrid law of expansion is also used to solve the field equations. Three different functional forms of the function $f(T)$ such as $f(T)=\eta {(-T)}^m+c,$$f(T)=e^{mT}$ and $f(T)=\gamma T+\eta T^m$ are chosen for investigation. It is observed that the universe is dominated by quintessence type dark energy. The universe is accelerating, expanding and anisotropic.

In this paper, we study the vacuum bosonic currents in the geometry of a compactified cosmic string in the background of the de Sitter spacetime. The currents are induced by magnetic fluxes, one running along the cosmic string and another one enclosed by the compact dimension. To develop the analysis, we obtain the complete set of normalized bosonic wave functions obeying a quasiperiodicity condition. In this context, we calculate the azimuthal and axial current densities and we show that these quantities are explicitly decomposed into two contributions: one originating from the geometry of a straight uncompactified cosmic string and the other induced by the compactification. We also compare the results with the literature in the case of a massive fermionic field in the same geometry.

We study the optical appearance of a thin accretion disk around a Schwarzschild black hole pierced by a cosmic string with a semi-analytic method of Luminet [Astron. Astrophys. 75 (1979) 228]. Direct and secondary images with different parameters observed by a distant observer are plotted. The cosmic string parameter $s$ can modify the shape and size of the thin disk image. We calculate and plot the distribution of both redshift and observed flux as seen by distant observers at different inclination angles. Those distributions are dependent on the inclination angle of the observer and cosmic string parameter $s$.

For the electromagnetic field in $(D+1)$-dimensional locally de Sitter (dS) spacetime, we analyze the effects of a generalized cosmic string type defect on the vacuum expectation value of the energy-momentum tensor. For the Bunch–Davies vacuum state, the topological contributions are explicitly extracted in both the diagonal and off-diagonal components. The latter describes the presence of radially directed energy flux in the vacuum state. It vanishes for $D=3$ because of the conformal invariance of the electromagnetic field and is directed towards the cosmic string for $D\ge 4$. The topological contributions in the vacuum stresses are anisotropic and, unlike the geometry of a cosmic string in the Minkowski spacetime, for $D>3$ the stresses along the directions parallel to the string core differ from the energy density. Depending on the planar angle deficit and the distance from the cosmic string, the corresponding expectation values can be either positive or negative. Near the cosmic string the effect of the gravitational field on the diagonal components of the topological part is weak and the leading terms in the respective expansions coincide with the expectation values for a cosmic string in the background of Minkowski spacetime. The spacetime curvature essentially modifies the behavior of the topological terms at proper distances from the cosmic string larger than the dS curvature radius. In that region, the topological contributions in the diagonal components of the energy–momentum tensor decay in inverse proportion to the fourth power of the proper distance and the energy flux density behaves as inverse-fifth power for all values of the spatial dimension $D$. The exception is the energy density in the special case $D=4$. For a cosmic string in the Minkowski bulk the energy flux is absent and the diagonal components are proportional to the $(D+1)$th power of the inverse distance.

In this paper, we investigate the relativistic harmonic oscillator in the Ellis–Bronnikov-type wormhole spacetime with a global monopole and cosmic string. We obtain the angular and radial wave functions exactly as well as the eigenenergies. Additionally, the radial wave function is expressed in terms of Heun polynomial, and as a consequence, the oscillation frequency is quantized. Finally, we graphically analyze the influence of the wormhole, as well as the influence of the global monopole and cosmic string on the radial probability density and the eigenenergies.

Magnetic fields can be generated in cosmic string wakes due to the Biermann mechanism in the presence of neutrino inhomogeneities. As the cosmic string moves through the plasma, the small magnetic field is amplified by the turbulence in the plasma. Relativistic charged particles which cross the magnetized wake of a cosmic string will therefore emit synchrotron radiation. The opening angle of the cosmic string is very small and so the wake appears like a thin sheet. Assuming a homogeneous magnetic field in the wake of the string, we obtain the synchrotron emission from nonthermal relativistic electrons in the wake of the string. The emitted radiation has a broad peak and is over a wide range of frequency. We show that the spectrum can be mapped to some of the unknown sources in different ranges of the current available catalogues.