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Using the Regge-Wheeler-Zerilli formalism of fully relativistic linear perturbations in

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The authors examine the gravitational coupling of Klein-Gordon and Dirac fields to matter vorticity and spacetime torsion, in the context of Einstein-Cartan theory. The background spacetime is endowed with a Godel-type metric, characterized by two real parameters ( Omega , l2); the source of spacetime curvature is a Weyssenhoff-Raabe fluid with spin vector parallel to the vorticity field. They show that torsion and matter vorticity have identical effects on the physics of particle fields. Complete sets of solutions are obtained, satisfying boundary conditions connected to the test-field character of the solutions. The energy spectrum obtained is discrete in general, except for the case of hyperbolic Godel-type geometries (l2>0) where a continuum region in the energy spectrum may appear: if 0< Omega 2or=l2, Dirac solutions may present, under certain conditions, a continuum region in the lower part of the spectrum. The correspondence between classical geodesic motion and Klein-Gordon solutions is established, and used as a guide to select the correct boundary conditions for the test fields. Matter vorticity and/or spacetime torsion split the energy spectrum of Dirac particles. These effects are additive and result from the existence of the same constant of motion for both cases. This constant of motion generates a trivial symmetry of the system in Minkowski spacetime, the associated degeneracy of which is raised by matter vorticity and/or torsion fields, producing the above-mentioned split.

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We present a complete study of geodesic motion in Godel's universe, using the method of the effective potential. A clear physical picture of free motion and its stability in this universe emerges. A large class of geodesics have finite intervals in which the particle moves back in time (dt/ds

A complete relativistic analysis for gravitational radiation emitted by a particle in circular orbit around a Schwarzschild black hole is presented in the Regge-Wheeler formalism. For completeness and contrast we also analyze the electromagnetic and scalar radiation emitted by a suitably charged particle. The three radiation spectra are drastically different. We stress some important consequences and astrophysical implications.It has been recently suggested by Misner, 1 Misner et al., 2 and Campbell and Matzner 3 that in the emission process of gravitational radiation, high beaming due to synchrotron effects could take place in extremely relativistic regimes. Indeed the existence of this phenomenon would be of great importance for experimental detection of gravitational radiation. The required total energy corresponding to an observed event may be very much smaller than usually estimated if (in order of importance !) (a) the beaming effect exists; (b) a privileged plane of emission is found for the beamed radiation; and (c) the detector happens to be in that plane. The failure to fulfill one of these three circumstances would make the phenomenon largely uninteresting. In this Letter we address ourselves to condition (a). We analyze the gravitational radiation emitted by a particle moving in the field of a Schwarzschild black hole in stable (r > 6M) as well as unstable (3M^r^6M) circular orbits (geometrical units, G = c = 1). To compare and contrast the results we also give the explicit analytic formulas and the energy fluxes for the cases of a charged particle emitting electromagnetic radiation (for details see Ruffini, Tiomno, and Vishveshwara, 4 Ruffini and Tiomno, 5 and Denardo, Ruffini, and Tiomno 6 ) and a particle 7 emitting scalar radiation in the same orbit. As a biproduct of our results it will become evident that an extrapolation from the results obtained in the case of scalar radiation to the case of gravitational synchrotron radiation does not properly account for the complexity of the tensor field. The complete treatment and details of these works will be pub-lished in later papers. 5 » 6 * 8 Before giving the main results of our treatment let us recall that the circular orbits between 3M