arXiv subjects
Publications and source records attributed to Patricio. S. Letelier.
We study a noncovariant theory of gravitation based on the Lagrangian density $\sqrt{-g})^ωR$, where $ω$ is a constant. In particular, we study solutions that for $ω=1$ reduces to the de Sitter, Kasner and LFRW (with perfect fluid with as a source). We also consider spherically symmetric solutions.
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.
Solutions to the Einstein equation that represent the superposition of static isolated bodies with axially symmetry are presented. The equations nonlinearity yields singular structures (strut and membranes) to equilibrate the bodies. The force on the strut like singularities is computed for a variety of situations. The superposition of a ring and a particle is studied in some detail