On Rumer’s Invariant Theory of Gravitational Waves

Propagation of gravitational potential and gravitational field-strength has been considered here on the basis of Rumer’s Invariant Theory of Gravitational Waves. Finally some special cases of weak field have been discusse

Non-radial oscillations of anisotropic neutron stars in the Cowling approximation

One of the most common assumptions in the study of neutron star models and their oscillations is that the pressure is isotopic, however there are arguments that this may not be correct. Thus in the present paper we make a first step towards studying the nonradial oscillations of neutron stars with an anisotropic pressure. We adopt the so-called Cowling approximation where the spacetime metric is kept fixed and the oscillation spectrum for the first few fluid modes is obtained. The effect of the anisotropy on the frequencies is apparent, although with the present results it might be hard to distinguish it from the changes in the frequencies caused by different equations of state.Comment: 17 pages, 8 figures; title changed, comments adde

Gravitational Lensing by Rotating Naked Singularities

We model massive compact objects in galactic nuclei as stationary, axially-symmetric naked singularities in the Einstein-massless scalar field theory and study the resulting gravitational lensing. In the weak deflection limit we study analytically the position of the two weak field images, the corresponding signed and absolute magnifications as well as the centroid up to post-Newtonian order. We show that there are a static post-Newtonian corrections to the signed magnification and their sum as well as to the critical curves, which are function of the scalar charge. The shift of the critical curves as a function of the lens angular momentum is found, and it is shown that they decrease slightingly for the weakly naked and vastly for the strongly naked singularities with the increase of the scalar charge. The point-like caustics drift away from the optical axis and do not depend on the scalar charge. In the strong deflection limit approximation we compute numerically the position of the relativistic images and their separability for weakly naked singularities. All of the lensing quantities are compared to particular cases as Schwarzschild and Kerr black holes as well as Janis--Newman--Winicour naked singularities.Comment: 35 pages, 30 figure

Quasinormal modes for the charged Vaidya metric

The scalar wave equation is considered in the background of a charged Vaidya metric in double null coordinates $(u,v)$ describing a non-stationary charged black hole with varying mass $m(v)$ and charge $q(v)$. The resulting time-dependent quasinormal modes are presented and analyzed. We show, in particular, that it is possible to identify some signatures in the quasinormal frequencies from the creation of a naked singularity.Comment: 4 pages. Prepared for the proceedings of the Spanish Relativity meeting (ERE2010), Granada, Spain, September 6-10, 201

The Birkhoff Theorem in Multidimensional Gravity

The validity conditions for the extended Birkhoff theorem in multidimensional gravity with $n$ internal spaces are formulated, with no restriction on space-time dimensionality and signature. Examples of matter sources and geometries for which the theorem is valid are given. Further generalization of the theorem is discussed.Comment: 8 page