On the Stability of Circular Orbits of Particles Moving around Black Holes Surrounded by Axially Symmetric Structures

The Rayleigh criterion is used to study the stability of circular orbits of particles moving around static black holes surrounded by different axially symmetric structures with reflection symmetry, like disks, rings and halos. We consider three models of disks one of infinite extension and two finite, and one model of rings. The halos are represented by external quadrupole moments (either oblate or prolate). Internal quadrupole perturbation (oblate and prolate) are also considered. For this class of disks the counter-rotation hypothesis implies that the stability of the disks is equivalent to the stability of test particles. The stability of Newtonian systems is also considered and compared with the equivalent relativistic situation. We find that the general relativistic dynamics favors the formation of rings.Comment: RevTex, 9 pages, 14 eps figs. Phys. Rev. D to appea

Riemann-Christoffel flows

A geometric flow based in the Riemann-Christoffel curvature tensor that in two dimensions has some common features with the usual Ricci flow is presented. For $n$ dimensional spaces this new flow takes into account all the components of the intrinsic curvature. For four dimensional Lorentzian manifolds it is found that the solutions of the Einstein equations associated to a "detonant" sphere of matter, as well, as a Friedman-Roberson-Walker cosmological model are examples of Riemann-Christoffel flows. Possible generalizations are mentioned.Comment: 3 pages, RevTex,small changes, Int. J. Theor. Phys. (in press

Spacetime Defects: Torsion Loops

Spacetimes with everywhere vanishing curvature tensor, but with torsion different from zero only on world sheets that represent closed loops in ordinary space are presented, also defects along open curves with end points at infinity are studied. The case of defects along timelike loops is also considered and the geodesics in these spaces are briefly discussed.Comment: 8 pages, LATE

Triaxial Analytical Potential-Density Pairs for Galaxies

We present two triaxial analytical potential-density pairs that can be viewed as generalized versions of the axisymmetric Miyamoto and Nagai and Satoh galactic models. These potential-density pairs may be useful models for galaxies with box-shaped bulges. The resulting mass density distributions are everywhere non-negative and free from singularities. Also, a few numerically calculated orbits for the Miyamoto and Nagai-like triaxial potential are presented.Comment: 9 pages, 4 figures, accepted for publication in PAS

Thin-disk models in an Integrable Weyl-Dirac theory

We construct a class of static, axially symmetric solutions representing razor-thin disks of matter in an Integrable Weyl-Dirac theory proposed in Found. Phys. 29, 1303 (1999). The main differences between these solutions and the corresponding general relativistic one are analyzed, focusing on the behavior of physical observables (rotation curves of test particles, density and pressure profiles). We consider the case in which test particles move on Weyl geodesics. The same rotation curve can be obtained from many different solutions of the Weyl-Dirac theory, although some of these solutions present strong qualitative differences with respect to the usual general relativistic model (such as the appearance a ring-like density profile). In particular, for typical galactic parameters all rotation curves of the Weyl-Dirac model present Keplerian fall-off. As a consequence, we conclude that a more thorough analysis of the problem requires the determination of the gauge function $\beta$ on galactic scales, as well as restrictions on the test-particle behavior under the action of the additional fields introduced by this theory.Comment: 18 pages, 3 figures; accepted in General Relativity and Gravitatio