A Comment on Bonnor-Steadman Closed Timelike Curves

The existence and stability closed timelike curves in a Bonnor-Ward spacetime without torsion line singularities is shown by exhibiting particular examples.Comment: 2 pages, RevTex, minor correction

Chaos in Periodically Perturbed Monopole + Quadrupole Like Potentials

The motion of a particle that suffers the influence of simple inner (outer) periodic perturbations when it evolves around a center of attraction modeled by an inverse square law plus a quadrupole-like term is studied. The equations of motion are used to reduce the Melnikov method to the study of simple graphics.Comment: 12 pages, 6 Postscript figure

Stability of Closed Timelike Geodesics

The existence and stability under linear perturbations of closed timelike geodesics (CTGs) in Bonnor-Ward spacetime is studied in some detail. Regions where the CTG exist and are linearly stable are exhibited.Comment: 5 pages, REvTex, discussion added. PLA, in pres

Quantum Singularities in Static Spacetimes

We review the mathematical framework necessary to understand the physical content of quantum singularities in static spacetimes. We present many examples of classical singular spacetimes and study their singularities by using wave packets satisfying Klein-Gordon and Dirac equations. We show that in many cases the classical singularities are excluded when tested by quantum particles but unfortunately there are other cases where the singularities remain from the quantum mechanical point of view. When it is possible we also find, for spacetimes where quantum mechanics does not exclude the singularities, the boundary conditions necessary to turn the spatial portion of the wave operator into self-adjoint and emphasize their importance to the interpretation of quantum singularities.Comment: 14 pages, section Quantum Singularities has been improve

Quantum Singularities in Spacetimes with Spherical and Cylindrical Topological Defects

Exact solutions of Einstein equations with null Riemman-Christoffel curvature tensor everywhere, except on a hypersurface, are studied using quantum particles obeying the Klein-Gordon equation. We consider the particular cases when the curvature is represented by a Dirac delta function with support either on a sphere or on a cylinder (spherical and cylindrical shells). In particular, we analyze the necessity of extra boundary conditions on the shells.Comment: 7 page,1 fig., Revtex, J. Math. Phys, in pres

On the integrability of halo dipoles in gravity

We stress that halo dipole components are nontrivial in core-halo systems in both Newton's gravity and General Relativity. To this end, we extend a recent exact relativistic model to include also a halo dipole component. Next, we consider orbits evolving in the inner vacuum between a monopolar core and a pure halo dipole and find that, while the Newtonian dynamics is integrable, its relativistic counterpart is chaotic. This shows that chaoticity due only to halo dipoles is an intrinsic relativistic gravitational effect.Comment: 9 pages, REVTEX, two postscript figures include

Stability of general relativistic Miyamoto-Nagai galaxies

The stability of a recently proposed general relativistic model of galaxies is studied in some detail. This model is a general relativistic version of the well known Miyamoto-Nagai model that represents well a thick galactic disk. The stability of the disk is investigated under a general first order perturbation keeping the spacetime metric frozen (no gravitational radiation is taken into account). We find that the stability is associated with the thickness of the disk. We have that flat galaxies have more not-stable modes than the thick ones i.e., flat galaxies have a tendency to form more complex structures like rings, bars and spiral arms.Comment: 11 pages, 5 figures, accepted for publication in MNRA

Chaos and Rotating Black Holes with Halos

The occurrence of chaos for test particles moving around a slowly rotating black hole with a dipolar halo is studied using Poincar\'e sections. We find a novel effect, particles with angular momentum opposite to the black hole rotation have larger chaotic regions in phase space than particles initially moving in the same direction.Comment: 9 pages, 4 Postscript figures. Phys. Rev. D, in pres