Higher Dimensional Cylindrical or Kasner Type Electrovacuum Solutions

We consider a D dimensional Kasner type diagonal spacetime where metric functions depend only on a single coordinate and electromagnetic field shares the symmetries of spacetime. These solutions can describe static cylindrical or cosmological Einstein-Maxwell vacuum spacetimes. We mainly focus on electrovacuum solutions and four different types of solutions are obtained in which one of them has no four dimensional counterpart. We also consider the properties of the general solution corresponding to the exterior field of a charged line mass and discuss its several properties. Although it resembles the same form with four dimensional one, there is a difference on the range of the solutions for fixed signs of the parameters. General magnetic field vacuum solution are also briefly discussed, which reduces to Bonnor-Melvin magnetic universe for a special choice of the parameters. The Kasner forms of the general solution are also presented for the cylindrical or cosmological cases.Comment: 16 pages, Revtex. Text and references are extended, Published versio

Bianchi Type-II String Cosmological Models in Normal Gauge for Lyra's Manifold with Constant Deceleration Parameter

The present study deals with a spatially homogeneous and anisotropic Bianchi-II cosmological models representing massive strings in normal gauge for Lyra's manifold by applying the variation law for generalized Hubble's parameter that yields a constant value of deceleration parameter. The variation law for Hubble's parameter generates two types of solutions for the average scale factor, one is of power-law type and other is of the exponential form. Using these two forms, Einstein's modified field equations are solved separately that correspond to expanding singular and non-singular models of the universe respectively. The energy-momentum tensor for such string as formulated by Letelier (1983) is used to construct massive string cosmological models for which we assume that the expansion ($\theta$) in the model is proportional to the component $\sigma^{1}_{~1}$ of the shear tensor $\sigma^{j}_{i}$. This condition leads to $A = (BC)^{m}$, where A, B and C are the metric coefficients and m is proportionality constant. Our models are in accelerating phase which is consistent to the recent observations. It has been found that the displacement vector $\beta$ behaves like cosmological term $\Lambda$ in the normal gauge treatment and the solutions are consistent with recent observations of SNe Ia. It has been found that massive strings dominate in the decelerating universe whereas strings dominate in the accelerating universe. Some physical and geometric behaviour of these models are also discussed.Comment: 24 pages, 10 figure

Convex regions of stationary spacetimes and Randers spaces. Applications to lensing and asymptotic flatness

By using Stationary-to-Randers correspondence (SRC), a characterization of light and time-convexity of the boundary of a region of a standard stationary (n+1)-spacetime is obtained, in terms of the convexity of the boundary of a domain in a Finsler n or (n+1)-space of Randers type. The latter convexity is analyzed in depth and, as a consequence, the causal simplicity and the existence of causal geodesics confined in the region and connecting a point to a stationary line are characterized. Applications to asymptotically flat spacetimes include the light-convexity of stationary hypersurfaces which project in a spacelike section of an end onto a sphere of large radius, as well as the characterization of their time-convexity with natural physical interpretations. The lens effect of both light rays and freely falling massive particles with a finite lifetime, (i.e. the multiplicity of such connecting curves) is characterized in terms of the focalization of the geodesics in the underlying Randers manifolds.Comment: AMSLaTex, 41 pages. v2 is a major revision: new discussions on physical applicability of the results, especially to asymptotically flat spacetimes; references adde

Characterizing the curvature and its first derivative for imperfect fluids

The curvature tensor and its derivatives up to any order can be covariantly characterized by a minimal set of spinor quantities. On the other hand it might be useful, particularly in cosmology, to describe the geometry of a spacetime in a (1+3) formalism, based on an invariantly defined fluid velocity. In this work, we consider an imperfect fluid possessing both isotropic and anisotropic pressure. For these fluids, we determine the (1+3) matter terms of the curvature as well as the parts of the first order covariant derivative of the curvature (∇R) determined pointwise by the matter via the Bianchi identities. Explicit relations between the set of such terms obtained from the (1+3) and spinor decomposition of ∇R are given. We show that in both sets there are 36 independent terms.info:eu-repo/semantics/publishedVersio