Torsional oscillations of magnetized relativistic stars

Strong magnetic fields in relativistic stars can be a cause of crust fracturing, resulting in the excitation of global torsional oscillations. Such oscillations could become observable in gravitational waves or in high-energy radiation, thus becoming a tool for probing the equation of state of relativistic stars. As the eigenfrequency of torsional oscillation modes is affected by the presence of a strong magnetic field, we study torsional modes in magnetized relativistic stars. We derive the linearized perturbation equations that govern torsional oscillations coupled to the oscillations of a magnetic field, when variations in the metric are neglected (Cowling approximation). The oscillations are described by a single two-dimensional wave equation, which can be solved as a boundary-value problem to obtain eigenfrequencies. We find that, in the non-magnetized case, typical oscillation periods of the fundamental     torsional modes can be nearly a factor of 2 larger for relativistic stars than previously computed in the Newtonian limit. For magnetized stars, we show that the influence of the magnetic field is highly dependent on the assumed magnetic field configuration, and simple estimates obtained previously in the literature cannot be used for identifying normal modes observationally.     

On Relativistic Equations of Motion of an Earth Satellite

For numerical integration of the geocentric equations of motion of Earth satellites in the general relativity framework one may choose now between rather simple equations involving in their relativistic dynamical part only the Earth-induced terms and very complicated equations taking into account the relativistic third-body action. However, it is possible quite easily to take into account the relativistic indirect third-body perturbations and to neglect much lesser direct third-body perturbations. Such approach is based on the use of the Newtonian third-body perturbations in geocentric variables with expressing them in the relativistic manner in terms of the barycentric arguments. Together with it, to extend the known results for the spheroid model of the Earth, the Earth-induced terms are treated in great detail by including the non-spin part of the Earth vector-potential and the Earth triaxial non-sphericity.This revised version was published online in October 2005 with corrections to the Cover Date.     

Hannay angles for relativistic polar orbits around an oblate spheroid

The Hannay adiabatic angles are computed for polar orbits in the gravitational field of an oblate spheroid described in the post-Newtonian framework of general relativity.     

Cosmological Constant, Minimal Mass and Electroweak Interaction

A lower bound for the mass of a rotating body is derived in the general relativity theory with positive cosmological term Λ. The bound suggests a neutrino rest mass ∼1 meV and a neutrino magnetic moment of 10⁻⁴¹ erg/gauss ∼ Planck's magnetic moment. A connection between gravity and electroweak interaction is suggested.     

The Momentum 4-Vector Imparted by Gravitational Waves in Bianchi-Type Metrics

Considering the Møller, Weinberg and Qadir-Sharif's definitions in general relativity, we find the momentum 4-vector of the closed universe based on the Bianchi-type metrics. The momentum 4-vector (due to matter plus fields) is found to be zero. This result supports the viewpoints of Albrow and Tryon and extends the previous works by Cooperstock–Israelit, Rosen, Johri et al., Banerjee–Sen and Vargas who investigated the problem of the energy in Friedmann–Robertson–Walker universe and Salt?-Havare who studied the problem of the energy-momentum of the viscous Kasner-type space-times.     

Can the bump in the composite spectrum of GRB 910503 be an emission line feature of gamma-ray bursts？

Appearing in the composite spectral data of BATSE, EGRET and COMPTEL for GRB 910503, there is a bump at around 1600 keV. We perform a statistical analysis on the spectral data, trying to find out if the bump could be accounted for by a blue-shifted and significantly broadened rest frame line due to the Doppler effect of an expanding fireball surface. We made an F-test and adopted previously proposed criteria. The study reveals that the criteria are well satisfied and the feature can be interpreted as the blue shifted 6.4 keV line. Prom the fit with this line taken into account, we find the Lorentz factor of this source to be P = 116-9+9 (at the 68% confident level,△x2 = 1) and the rest frame spectral peak energy to be E0,p- 2.96-0.18+0.24 keV. Although the existence of the emission line feature requires other independent tests to confirm, the analysis suggests that it is feasible to detect emission line features in the high energy range of GRB spectra when taking into account the Doppler effect of fireball expansion.     

General relativistic self-similar solutions in cosmology

We present general relativistic solutions for self-similar spherical perturbations in an expanding cosmological background of cold pressure-less gas. We focus on solutions having shock discontinuities propagating in the surrounding cold gas. The pressure, p , and energy density, μ, in the shock-heated matter are assumed to obey   p = w μ  , where w is a positive constant. Consistent solutions are found for shocks propagating from the symmetry centre of a region of a positive density excess over the background. In these solutions, shocks exist outside the radius marking the event horizon of the black hole which would be present in a shock-less collapse. For large jumps in the energy density at the shock, a black hole is avoided altogether and the solutions are regular at the centre. The shock-heated gas does not contain any sonic points, provided the motion of the cold gas ahead of the shock deviates significantly from the Hubble flow. For shocks propagating in the uniform background, sonic points always appear for small jumps in the energy density. We also discuss self-similar solutions without shocks in fluids with   w < −1/3  .