A rotating cylinder in an asymptotically locally anti-de Sitter background

A family of exact solutions is presented which represents a rigidly rotating cylinder of dust in a background with a negative cosmological constant. The interior of the infinite cylinder is described by the Godel solution. An exact solution for the exterior solution is found which depends both on the rotation of the interior and on its radius. For values of these parameters less than a certain limit, the exterior solution is shown to be locally isomorphic to the Linet-Tian solution. For values larger than another limit, it is shown that the exterior solution extends into a region which contains closed timelike curves. At large distances from the source, the space-time is shown to be asymptotic locally to anti-de Sitter space.Comment: To appear in Classical and Quantum Gravit

Shear-free and homology conditions for self-gravitating dissipative fluids

The shear free condition is studied for dissipative relativistic self-gravitating fluids in the quasi-static approximation. It is shown that, in the Newtonian limit, such condition implies the linear homology law for the velocity of a fluid element, only if homology conditions are further imposed on the temperature and the emission rate. It is also shown that the shear-free plus the homogeneous expansion rate conditions are equivalent (in the Newtonian limit) to the homology conditions. Deviations from homology and their prospective applications to some astrophysical scenarios are discussed, and a model is worked out.Comment: 13 pages Latex. To apppear in Month.Not.Roy.Astr.Soc. Corrected typo

Cylindrical Collapse and Gravitational Waves

We study the matching conditions for a collapsing anisotropic cylindrical perfect fluid, and we show that its radial pressure is non zero on the surface of the cylinder and proportional to the time dependent part of the field produced by the collapsing fluid. This result resembles the one that arises for the radiation - though non-gravitational - in the spherically symmetric collapsing dissipative fluid, in the diffusion approximation.Comment: Some comments and a new reference added. To appear in Class. Quantum. Gra

Kerr Geodesics Following the Axis of Symmetry

We present here the general expressions for the acceleration of massive test particles along the symmetry axis of the Kerr metric, and then study the main properties of this acceleration in different regions of the spacetime. In particular, we show that there exists a region near the black hole in which the gravitational field is repulsive. We provide possible physical interpretations about the role of this effect in terms of the different conserved parameters. The studies of these geodesics are important not only to understand better the structure of the Kerr spacetime but also to its use as a possible mechanism for the production of extragalactic jets. Our results are obtained with the help of expressing the geodesics of the Kerr spacetime in terms of the Weyl coordinates.Comment: revtex4, no figures and tables. Gen. Relativ. Grav. 48 (2016) 6

The Levi-Civita spacetime as a limiting case of the Gamma spacetime

It is shown that the Levi-Civita metric can be obtained from a family of the Weyl metric, the Gamma metric, by taking the limit when the length of its Newtonian image source tends to infinity. In this process a relationship appears between two fundamental parameters of both metrics.Comment: LaTeX2e 17 page

Two 3-Branes in Randall-Sundrum Setup and Current Acceleration of the Universe

Five-dimensional spacetimes of two orbifold 3-branes are studied, by assuming that {\em the two 3-branes are spatially homogeneous, isotropic, and independent of time}, following the so-called "bulk-based" approach. The most general form of the metric is obtained, and the corresponding field equations are divided into three groups, one is valid on each of the two 3-branes, and the third is valid in the bulk. The Einstein tensor on the 3-branes is expressed in terms of the discontinuities of the first-order derivatives of the metric coefficients. Thus, once the metric is known in the bulk, the distribution of the Einstein tensor on the two 3-branes is uniquely determined. As applications, we consider two different cases, one is in which the bulk is locally $AdS_{5}$, and the other is where it is vacuum. In some cases, it is shown that the universe is first decelerating and then accelerating. The global structure of the bulk as well as the 3-branes is also studied, and found that in some cases the solutions may represent the collision of two orbifold 3-branes. The applications of the formulas to the studies of the cyclic universe and the cosmological constant problem are also pointed out.Comment: revtex4, 14 figures, published in Nucl. Phys. B797 (2008) 395 - 43