Stably stratified stars containing magnetic fields whose toroidal components are much larger than the poloidal ones in general relativity: A perturbation analysis

We construct the stably stratified magnetized stars within the framework of general relativity. The effects of magnetic fields on the structure of the star and spacetime are treated as perturbations of non-magnetized stars. By assuming ideal magnetohydrodynamics and employing one-parameter equations of state, we derive basic equations for describing stationary and axisymmetric stably stratified stars containing magnetic fields whose toroidal components are much larger than the poloidal ones. A number of the polytropic models are numerically calculated to investigate basic properties of the effects of magnetic fields on the stellar structure. According to the stability result obtained by Braithwaite, which remains a matter of conjecture for general magnetized stars, certain of the magnetized stars constructed in this study are possibly stable.Comment: 23 pages, 11 figures. arXiv admin note: text overlap with arXiv:1207.194

Accuracy of the relativistic Cowling approximation in slowly rotating stars

We have calculated the non-radial oscillation in slowly rotating relativistic stars with the Cowling approximation. The frequencies are compared with those based on the complete linearized equations of general relativity. It is found that the results with the approximation differ by less than about $20$ for typical relativistic stellar models. The approximation is more accurate for higher-order modes as in the Newtonian case.Comment: 5 pages, LaTeX, 3 figures, to appear in Mon. Not. R. Astron. So

Possible measurement of Quintessence and density parameter using strong gravitational lensing events

We propose a possible measurement of the time variability of the vacuum energy using strong gravitational lensing events. As an example we take an Einstein cross lens HST 14176+5226 and demonstrate that the measurement of the velocity dispersion with the accuracy of $\pm$ 5 km/sec will have a chance to determine the time dependence of the vacuum energy as well as the density parameter with the accuracy of order 0.1 if one fixes the lens model.Comment: 5 pages, 1 figure, accepted for publication in Progress of Theoretical Physic