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

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.

Probing Strong-Field Scalar-Tensor Gravity with Gravitational Wave Asteroseismology

We present an alternative way of tracing the existence of a scalar field based on the analysis of the gravitational wave spectrum of a vibrating neutron star. Scalar-tensor theories in strong-field gravity can potentially introduce much greater differences in the parameters of a neutron star than the uncertainties introduced by the various equations of state. The detection of gravitational waves from neutron stars can set constraints on the existence and the strength of scalar fields. We show that the oscillation spectrum is dramatically affected by the presence of a scalar field, and can provide unique confirmation of its existence.Comment: 14 pages, 7 figure

Gravitational waves from pulsations of neutron stars described by realistic Equations of State

In this work we discuss the time-evolution of nonspherical perturbations of a nonrotating neutron star described by a realistic Equation of State (EOS). We analyze 10 different EOS for a large sample of neutron star models. Various kind of generic initial data are evolved and the corresponding gravitational wave signals are computed. We focus on the dynamical excitation of fluid and spacetime modes and extract the corresponding frequencies. We employ a constrained numerical algorithm based on standard finite differencing schemes which permits stable and long term evolutions. Our code provides accurate waveforms and allows to capture, via Fourier analysis of the energy spectra, the frequencies of the fluid modes with an accuracy comparable to that of frequency domain calculations. The results we present here are useful for provindig comparisons with simulations of nonlinear oscillations of (rotating) neutron star models as well as testbeds for 3D nonlinear codes.Comment: 17 pages, 9 figures. Small changes. Version published in Phys. Rev.

Gravitational radiation from collapsing magnetized dust

In this article we study the influence of magnetic fields on the axial gravitational waves emitted during the collapse of a homogeneous dust sphere. We found that while the energy emitted depends weakly on the initial matter perturbations it has strong dependence on the strength and the distribution of the magnetic field perturbations. The gravitational wave output of such a collapse can be up to an order of magnitude larger or smaller calling for detailed numerical 3D studies of collapsing magnetized configurations

Quasinormal Modes of Charged Scalars around Dilaton Black Holes in 2+1 Dimensions: Exact Frequencies

We have studied the charged scalar perturbation around a dilaton black hole in 2 +1 dimensions. The wave equations of a massless charged scalar field is shown to be exactly solvable in terms of hypergeometric functions. The quasinormal frequencies are computed exactly. The relation between the quasinormal frequencies and the charge of the black hole, charge of the scalar and the temperature of the black hole are analyzed. The asymptotic form of the real part of the quasinormal frequencies are evaluated exactly.Comment: 20 pages and 7 figures, some references are added and some removed. There are some changes to the text. arXiv admin note: text overlap with arXiv:hep-th/040716

Determination of the internal structure of neutron stars from gravitational wave spectra

In this paper the internal structure of a neutron star is shown to be inferrable from its gravitational-wave spectrum. Iteratively applying the inverse scheme of the scaled coordinate logarithmic perturbation method for neutron stars proposed by Tsui and Leung [Astrophys. J. {\bf 631}, 495 (2005)], we are able to determine the mass, the radius and the mass distribution of a star from its quasi-normal mode frequencies of stellar pulsation. In addition, accurate equation of state of nuclear matter can be obtained from such inversion scheme. Explicit formulas for the case of axial $w$-mode oscillation are derived here and numerical results for neutron stars characterized by different equations of state are shown.Comment: 26 pages, 14 figures, submitted to Physical Review

Equivariant wave maps exterior to a ball

We consider the exterior Cauchy-Dirichlet problem for equivariant wave maps from 3+1 dimensional Minkowski spacetime into the three-sphere. Using mixed analytical and numerical methods we show that, for a given topological degree of the map, all solutions starting from smooth finite energy initial data converge to the unique static solution (harmonic map). The asymptotics of this relaxation process is described in detail. We hope that our model will provide an attractive mathematical setting for gaining insight into dissipation-by-dispersion phenomena, in particular the soliton resolution conjecture.Comment: 16 pages, 9 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

Close-limit analysis for head-on collision of two black holes in higher dimensions: Brill-Lindquist initial data

Motivated by the TeV-scale gravity scenarios, we study gravitational radiation in the head-on collision of two black holes in higher dimensional spacetimes using a close-limit approximation. We prepare time-symmetric initial data sets for two black holes (the so-called Brill-Lindquist initial data) and numerically evolve the spacetime in terms of a gauge invariant formulation for the perturbation around the higher-dimensional Schwarzschild black holes. The waveform and radiated energy of gravitational waves emitted in the head-on collision are clarified. Also, the complex frequencies of fundamental quasinormal modes of higher-dimensional Schwarzschild black holes, which have not been accurately derived so far, are determined.Comment: 27 pages, 8 figures, published versio