Segre Types of Symmetric Two-tensors in n-Dimensional Spacetimes

Three propositions about Jordan matrices are proved and applied to algebraically classify the Ricci tensor in n-dimensional Kaluza-Klein-type spacetimes. We show that the possible Segre types are [1,1...1], [21...1], [31\ldots 1], [z\bar{z}1...1] and degeneracies thereof. A set of canonical forms for the Segre types is obtained in terms of semi-null bases of vectors.Comment: 14 pages, LaTeX, replaced due to a LaTex erro

Riemann-Cartan Space-times of G\"odel Type

A class of Riemann-Cartan G\"odel-type space-times are examined in the light of the equivalence problem techniques. The conditions for local space-time homogeneity are derived, generalizing previous works on Riemannian G\"odel-type space-times. The equivalence of Riemann-Cartan G\"odel-type space-times of this class is studied. It is shown that they admit a five-dimensional group of affine-isometries and are characterized by three essential parameters $\ell, m^2, \omega$: identical triads ($\ell, m^2, \omega$) correspond to locally equivalent manifolds. The algebraic types of the irreducible parts of the curvature and torsion tensors are also presented.Comment: 24 pages, LaTeX fil

Collimation of a spherical collisionless particles stream in Kerr space-time

We examine the propagation of collisionless particles emitted from a spherical shell to infinity. The number distribution at infinity, calculated as a function of the polar angle, exhibits a small deviation from uniformity. The number of particles moving from the polar region toward the equatorial plane is slightly larger than that of particles in the opposite direction, for an emission radius $> 4.5M$ in extreme Kerr space-time. This means that the black hole spin exerts an anti-collimation effect on the particles stream propagating along the rotation axis. We also confirm this property in the weak field limit. The quadrupole moment of the central object produces a force toward the equatorial plane. For a smaller emission radius $r<4.5M$, the absorption of particles into the black hole, the non-uniformity and/or the anisotropy of the emission distribution become much more important.Comment: 11 pages, 8 figures; accepted for publication in CQ

Unstable fields in Kerr spacetimes

We show that both the interior region $r<M-\sqrt{M^2-a^2}$ of a Kerr black hole and the $a^2>M^2$ Kerr naked singularity admit unstable solutions of the Teukolsky equation for any value of the spin weight. For every harmonic number there is at least one axially symmetric mode that grows exponentially in time and decays properly in the radial directions. These can be used as Debye potentials to generate solutions for the scalar, Weyl spinor, Maxwell and linearized gravity field equations on these backgrounds, satisfying appropriate spatial boundary conditions and growing exponentially in time, as shown in detail for the Maxwell case. It is suggested that the existence of the unstable modes is related to the so called "time machine" region, where the axial Killing vector field is time-like, and the Teukolsky equation, restricted to axially symmetric fields, changes its character from hyperbolic to elliptic

Bianchi I Quantum cosmology in the Bergmann-Wagoner theory

The Wheeler-DeWitt equation is considered in the context of generalized scalar-tensor theories of gravitation for Bianchi type I cosmology. Exact solutions are found for two selfinteracting potentials and arbitary coupling function. The WKB wavefunctions are obtained and a family of solutions satisfying the Hawking-Page regularity conditions of wormholes are found.Comment: 12 pages, Latex fil

On the propagation of jump discontinuities in relativistic cosmology

A recent dynamical formulation at derivative level \ptl^{3}g for fluid spacetime geometries $({\cal M}, {\bf g}, {\bf u})$, that employs the concept of evolution systems in first-order symmetric hyperbolic format, implies the existence in the Weyl curvature branch of a set of timelike characteristic 3-surfaces associated with propagation speed |v| = \sfrac{1}{2} relative to fluid-comoving observers. We show it is the physical role of the constraint equations to prevent realisation of jump discontinuities in the derivatives of the related initial data so that Weyl curvature modes propagating along these 3-surfaces cannot be activated. In addition we introduce a new, illustrative first-order symmetric hyperbolic evolution system at derivative level \ptl^{2}g for baryotropic perfect fluid cosmological models that are invariant under the transformations of an Abelian $G_{2}$ isometry group.Comment: 19 pages, 1 table, REVTeX v3.1 (10pt), submitted for publication to Physical Review D; added Report-No, corrected typo

Gravastar energy conditions revisited

We consider the gravastar model where the vacuum phase transition between the de Sitter interior and the Schwarzschild or Schwarzschild-de Sitter exterior geometries takes place at a single spherical delta-shell. We derive sharp analytic bounds on the surface compactness (2m/r) that follow from the requirement that the dominant energy condition (DEC) holds at the shell. In the case of Schwarzschild exterior, the highest surface compactness is achieved with the stiff shell in the limit of vanishing (dark) energy density in the interior. In the case of Schwarzschild-de Sitter exterior, in addition to the gravastar configurations with the shell under surface pressure, gravastar configurations with vanishing shell pressure (dust shells), as well as configurations with the shell under surface tension, are allowed by the DEC. Respective bounds on the surface compactness are derived for all cases. We also consider the speed of sound on the shell as derived from the requirement that the shell is stable against the radial perturbations. The causality requirement (sound speed not exceeding that of light) further restricts the space of allowed gravastar configurations.Comment: LaTeX/IOP-style, 16 pages, 2 figures, changes wrt v1: motivation for eq. (6) clarified, several referecnes added (to appear in Class. Quantum Grav.

On rigidly rotating perfect fluid cylinders

The gravitational field of a rigidly rotating perfect fluid cylinder with gamma- law equation of state is found analytically. The solution has two parameters and is physically realistic for gamma in the interval (1.41,2]. Closed timelike curves always appear at large distances.Comment: 10 pages, Revtex (galley

Density growth in Kantowski-Sachs cosmologies with cosmological constant

In this work the growth of density perturbations in Kantowski-Sachs cosmologies with a positive cosmological constant is studied, using the 1+3 and 1+1+2 covariant formalisms. For each wave number we obtain a closed system for scalars formed from quantities that are zero on the background and hence are gauge-invariant. The solutions to this system are then analyzed both analytically and numerically. In particular the effects of anisotropy and the behaviour close to a bounce in the cosmic scale factor are considered. We find that typically the density gradient in the bouncing directions experiences a local maximum at or slightly after the bounce.Comment: 33 pages, 17 picture

Vacuum Plane Waves in 4+1 D and Exact solutions to Einstein's Equations in 3+1 D

In this paper we derive homogeneous vacuum plane-wave solutions to Einstein's field equations in 4+1 dimensions. The solutions come in five different types of which three generalise the vacuum plane-wave solutions in 3+1 dimensions to the 4+1 dimensional case. By doing a Kaluza-Klein reduction we obtain solutions to the Einstein-Maxwell equations in 3+1 dimensions. The solutions generalise the vacuum plane-wave spacetimes of Bianchi class B to the non-vacuum case and describe spatially homogeneous spacetimes containing an extremely tilted fluid. Also, using a similar reduction we obtain 3+1 dimensional solutions to the Einstein equations with a scalar field.Comment: 16 pages, no figure