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

Geodesics in Lewis Spacetime

The geodesic equations are integrated for the Lewis metric and the effects of the different parameters appearing in the Weyl class on the motion of test particles are brought out. Particular attention deserves the appearance of a force parallel to the axial axis and without Newtonian analogue.Comment: 15 pages, Late

On the gravitomagnetic effects in cylindrically symmetric spacetimes

Using gyroscopes we generalize results, obtained for the gravitomagnetic clock effect in the particular case when the exterior spacetime is produced by a rotating dust cylinder, to the case when the vacuum spacetime is described by the general cylindrically symmetric Lewis spacetime. Results are contrasted with those obtained for the Kerr spacetime.Comment: 11 pages Latex, to appear in J.Math.Phy

Collapsing Spheres Satisfying An "Euclidean Condition"

We study the general properties of fluid spheres satisfying the heuristic assumption that their areas and proper radius are equal (the Euclidean condition). Dissipative and non-dissipative models are considered. In the latter case, all models are necessarily geodesic and a subclass of the Lemaitre-Tolman-Bondi solution is obtained. In the dissipative case solutions are non-geodesic and are characterized by the fact that all non-gravitational forces acting on any fluid element produces a radial three-acceleration independent on its inertial mass.Comment: 1o pages, Latex. Title changed and text shortened to fit the version to appear in Gen.Rel.Grav

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

On the compressibility equation of state for multicomponent adhesive hard sphere fluids

The compressibility equation of state for a multicomponent fluid of particles interacting via an infinitely narrow and deep potential, is considered within the mean spherical approximation (MSA). It is shown that for a class of models leading to a particular form of the Baxter functions $q_{ij}(r)$ containing density-independent stickiness coefficient, the compressibility EOS does not exist, unlike the one-component case. The reason for this is that a direct integration of the compressibility at fixed composition, cannot be carried out due to the lack of a reciprocity relation on the second order partial derivatives of the pressure with respect to two different densities. This is, in turn, related to the inadequacy of the MSA. A way out to this drawback is presented in a particular example, leading to a consistent compressibility pressure, and a possible generalization of this result is discussed.Comment: 13 pages, no figures, accepted for publication Molec. Physics (2002