The inverse problem for pulsating neutron stars: A ``fingerprint analysis'' for the supranuclear equation of state

We study the problem of detecting, and infering astrophysical information from, gravitational waves from a pulsating neutron star. We show that the fluid f and p-modes, as well as the gravitational-wave w-modes may be detectable from sources in our own galaxy, and investigate how accurately the frequencies and damping rates of these modes can be infered from a noisy gravitational-wave data stream. Based on the conclusions of this discussion we propose a strategy for revealing the supranuclear equation of state using the neutron star fingerprints: the observed frequencies of an f and a p-mode. We also discuss how well the source can be located in the sky using observations with several detectors.Comment: 9 pages, 3 figure

Asymptotic quasinormal modes of Reissner-Nordstr\"om and Kerr black holes

According to a recent proposal, the so-called Barbero-Immirzi parameter of Loop Quantum Gravity can be fixed, using Bohr's correspondence principle, from a knowledge of highly-damped black hole oscillation frequencies. Such frequencies are rather difficult to compute, even for Schwarzschild black holes. However, it is now quite likely that they may provide a fundamental link between classical general relativity and quantum theories of gravity. Here we carry out the first numerical computation of very highly damped quasinormal modes (QNM's) for charged and rotating black holes. In the Reissner-Nordstr\"om case QNM frequencies and damping times show an oscillatory behaviour as a function of charge. The oscillations become faster as the mode order increases. At fixed mode order, QNM's describe spirals in the complex plane as the charge is increased, tending towards a well defined limit as the hole becomes extremal. Kerr QNM's have a similar oscillatory behaviour when the angular index $m=0$. For $l=m=2$ the real part of Kerr QNM frequencies tends to $2\Omega$, $\Omega$ being the angular velocity of the black hole horizon, while the asymptotic spacing of the imaginary parts is given by $2\pi T_H$.Comment: 13 pages, 7 figures. Added result on the asymptotic spacing of the imaginary part, minor typos correcte

Scattering of particles by neutron stars: Time-evolutions for axial perturbations

The excitation of the axial quasi-normal modes of a relativistic star by scattered particles is studied by evolving the time dependent perturbation equations. This work is the first step towards the understanding of more complicated perturbative processes, like the capture or the scattering of particles by rotating stars. In addition, it may serve as a test for the results of the full nonlinear evolution of binary systems.Comment: 7 pages, 5 figures, Phys. Rev. D in pres

Gravitational waves from a test particle scattered by a neutron star: Axial mode case

Using a metric perturbation method, we study gravitational waves from a test particle scattered by a spherically symmetric relativistic star. We calculate the energy spectrum and the waveform of gravitational waves for axial modes. Since metric perturbations in axial modes do not couple to the matter fluid of the star, emitted waves for a normal neutron star show only one peak in the spectrum, which corresponds to the orbital frequency at the turning point, where the gravitational field is strongest. However, for an ultracompact star (the radius $R \lesssim 3M$), another type of resonant periodic peak appears in the spectrum. This is just because of an excitation by a scattered particle of axial quasinormal modes, which were found by Chandrasekhar and Ferrari. This excitation comes from the existence of the potential minimum inside of a star. We also find for an ultracompact star many small periodic peaks at the frequency region beyond the maximum of the potential, which would be due to a resonance of two waves reflected by two potential barriers (Regge-Wheeler type and one at the center of the star). Such resonant peaks appear neither for a normal neutron star nor for a Schwarzschild black hole. Consequently, even if we analyze the energy spectrum of gravitational waves only for axial modes, it would be possible to distinguish between an ultracompact star and a normal neutron star (or a Schwarzschild black hole).Comment: 21 pages, revtex, 11 figures are attached with eps files Accepted to Phys. Rev.

Quasinormal Modes, the Area Spectrum, and Black Hole Entropy

The results of canonical quantum gravity concerning geometric operators and black hole entropy are beset by an ambiguity labelled by the Immirzi parameter. We use a result from classical gravity concerning the quasinormal mode spectrum of a black hole to fix this parameter in a new way. As a result we arrive at the Bekenstein - Hawking expression of $A/4 l_P^2$ for the entropy of a black hole and in addition see an indication that the appropriate gauge group of quantum gravity is SO(3) and not its covering group SU(2).Comment: 4 pages, 2 figure

Quasinormal behavior of the D-dimensional Schwarzshild black hole and higher order WKB approach

We study characteristic (quasinormal) modes of a $D$-dimensional Schwarzshild black hole. It proves out that the real parts of the complex quasinormal modes, representing the real oscillation frequencies, are proportional to the product of the number of dimensions and inverse horizon radius $\sim D r_{0}^{-1}$. The asymptotic formula for large multipole number $l$ and arbitrary $D$ is derived. In addition the WKB formula for computing QN modes, developed to the 3rd order beyond the eikonal approximation, is extended to the 6th order here. This gives us an accurate and economic way to compute quasinormal frequencies.Comment: 15 pages, 6 figures, the 6th order WKB formula for computing QNMs in Mathematica is available from https://goo.gl/nykYG

Phenomenological Relations for Axial Quasi-normal Modes of Neutron Stars with Realistic Equations of State

Here we investigate the axial w quasi-normal modes of neutron stars for several equations of state. In particular, we study the influence of the presence of hyperons in the core of the neutron stars. We have obtained that w-modes can be used to distinguish between neutron stars with hyperons and without hyperons for compact enough stars. We present phenomenological relations for the frequency and damping times with the compactness of the neutron star for wI and wII modes showing the differences of the stars with hyperons in the core. Also, we obtain a new phenomenological relation between the real part and the imaginary part of the frequency of the w quasi-normal modes, which can be used to estimate the central pressure of the neutron stars. We are able to construct explicitly the low compactness limit configuration for which the fundamental wII mode vanishes. Finally, we have studied the influence of changes in the core-crust transition pressure obtaining that it is very small. To obtain these results we have developed a new method based on the Exterior Complex Scaling technique with variable angle, appropriate for the treatment of the exterior part of the quasi-normal modes, which allow us to impose constringent enough conditions to generate pure outgoing quasi-normal modes. For the interior part we use a piece-wise polytrope approximation for several equations of state. A complete study of the junction conditions have been done.Comment: 17 pages, 16 figures, 3 table

Trapped gravitational wave modes in stars with R>3M

The possibility of trapped modes of gravitational waves appearing in stars with R>3M is considered. It is shown that the restriction to R<3M in previous studies of trapped modes, using uniform density models, is not essential. Scattering potentials are computed for another family of analytic stellar models showing the appearance of a deep potential well for one model with R>3M. However, the provided example is unstable, although it has a more realistic equation of state in the sense that the sound velocity is finite. On the other hand it is also shown that for some stable models belonging to the same family but having R<3M, the well is significantly deeper than that of the uniform density stars. Whether there are physically realistic equations of state which allow stable configurations with trapped modes therefore remains an open problem.Comment: 10 pages, 3 figures, LaTeX2