Oscillations of rapidly rotating relativistic stars

Non-axisymmetric oscillations of rapidly rotating relativistic stars are studied using the Cowling approximation. The oscillation spectra have been estimated by Fourier transforming the evolution equations describing the perturbations. This is the first study of its kind and provides information on the effect of fast rotation on the oscillation spectra while it offers the possibility in studying the complete problem by including spacetime perturbations. Our study includes both axisymmetric and non-axisymmetric perturbations and provides limits for the onset of the secular bar mode rotational instability. We also present approximate formulae for the dependence of the oscillation spectrum from rotation. The results suggest that it is possible to extract the relativistic star's parameters from the observed gravitational wave spectrum.Comment: this article will be published in Physical Review

Instabilities of Relativistic Stars

Recent developments on the rotational instabilities of relativistic stars are reviewed. The article provides an account of the theory of stellar instabilities with emphasis on the rotational ones. Special attention is being paid to the study of these instabilities in the general relativistic regime. Issues such as the existence relativistic r-modes, the existence of a continuous spectrum and the CFS instability of the w-modes are discussed in the second half of the article.Comment: 41 pages, 12 figures, Proceedings of the 25th John Hopkins Workshop, Florenc

Analytic description of the r-mode instability in uniform density stars

We present an analytic description of the $r$-mode instability in newly-born neutron stars, using the approximation of uniform density. Our computation is consistently accurate to second order in the angular velocity of the star. We obtain formulae for the growth-time of the instability due to gravitational-wave emission, for both current and mass multipole radiation and for the damping timescale, due to viscosity. The $l=m=2$ current-multipole radiation dominates the timescale of the instability. We estimate the deviation of the second order accurate results from the lowest order approximation and show that the uncertainty in the equation of state has only a small effect on the onset of the $r$-mode instability. The viscosity coefficients and the cooling process in newly-born neutron stars are, at present, uncertain and our analytic formaulae enables a quick check of such effects on the development of the instability.Comment: 7 pages, 2 figure

On the r-mode spectrum of relativistic stars

We present a mathematically rigorous proof that the r-mode spectrum of relativistic stars to the rotational lowest order has a continuous part. A rigorous definition of this spectrum is given in terms of the spectrum of a continuous linear operator. This study verifies earlier results by Kojima (1998) about the nature of the r-mode spectrum.Comment: 6 pages, no figure

Perturbative Analysis of Universality and Individuality in Gravitational Waves from Neutron Stars

The universality observed in gravitational wave spectra of non-rotating neutron stars is analyzed here. We show that the universality in the axial oscillation mode can be reproduced with a simple stellar model, namely the centrifugal barrier approximation (CBA), which captures the essence of the Tolman VII model of compact stars. Through the establishment of scaled co-ordinate logarithmic perturbation theory (SCLPT), we are able to explain and quantitatively predict such universal behavior. In addition, quasi-normal modes of individual neutron stars characterized by different equations of state can be obtained from those of CBA with SCLPT.Comment: 29 pages, 10 figures, submitted to Astrophysical Journa

Workshop on gravitational waves

In this article we summarise the proceedings of the Workshop on Gravitational Waves held during ICGC-95. In the first part we present the discussions on 3PN calculations (L. Blanchet, P. Jaranowski), black hole perturbation theory (M. Sasaki, J. Pullin), numerical relativity (E. Seidel), data analysis (B.S. Sathyaprakash), detection of gravitational waves from pulsars (S. Dhurandhar), and the limit on rotation of relativistic stars (J. Friedman). In the second part we briefly discuss the contributed papers which were mainly on detectors and detection techniques of gravitational waves.Comment: 18 pages, kluwer.sty, no figure

Non-Schwarzschild black-hole metric in four dimensional higher derivative gravity: analytical approximation

Higher derivative extensions of Einstein gravity are important within the string theory approach to gravity and as alternative and effective theories of gravity. H. L\"u, A. Perkins, C. Pope, K. Stelle [Phys.Rev.Lett. 114 (2015), 171601] found a numerical solution describing a spherically symmetric non-Schwarzschild asymptotically flat black hole in the Einstein gravity with added higher derivative terms. Using the general and quickly convergent parametrization in terms of the continued fractions, we represent this numerical solution in the analytical form, which is accurate not only near the event horizon or far from black hole, but in the whole space. Thereby, the obtained analytical form of the metric allows one to study easily all the further properties of the black hole, such as thermodynamics, Hawking radiation, particle motion, accretion, perturbations, stability, quasinormal spectrum, etc. Thus, the found analytical approximate representation can serve in the same way as an exact solution.Comment: 9 pages, 4 figures, 1 ancillary Mathematica(R) noteboo

Dynamical excitation of space-time modes of compact objects

We discuss, in the perturbative regime, the scattering of Gaussian pulses of odd-parity gravitational radiation off a non-rotating relativistic star and a Schwarzschild Black Hole. We focus on the excitation of the $w$-modes of the star as a function of the width $b$ of the pulse and we contrast it with the outcome of a Schwarzschild Black Hole of the same mass. For sufficiently narrow values of $b$, the waveforms are dominated by characteristic space-time modes. On the other hand, for sufficiently large values of $b$ the backscattered signal is dominated by the tail of the Regge-Wheeler potential, the quasi-normal modes are not excited and the nature of the central object cannot be established. We view this work as a useful contribution to the comparison between perturbative results and forthcoming $w$-mode 3D-nonlinear numerical simulation.Comment: RevTeX, 9 pages, 7 figures, Published in Phys. Rev.