Quasinormal modes and stability of the rotating acoustic black hole: numerical analysis

The study of the quasinormal modes (QNMs) of the 2+1 dimensional rotating draining bathtub acoustic black hole, the closest analogue found so far to the Kerr black hole, is performed. Both the real and imaginary parts of the quasinormal (QN) frequencies as a function of the rotation parameter B are found through a full non-linear numerical analysis. Since there is no change in sign in the imaginary part of the frequency as B is increased we conclude that the 2+1 dimensional rotating draining bathtub acoustic black hole is stable against small perturbations.Comment: 6 pages, ReVTeX4. v2. References adde

Detection of Gravitational Waves from the Coalescence of Population-III Remnants with Advanced LIGO

The comoving mass density of massive black hole (MBH) remnants from pre-galactic star formation could have been similar in magnitude to the mass-density of supermassive black holes (SMBHs) in the present-day universe. We show that the fraction of MBHs that coalesce during the assembly of SMBHs can be extracted from the rate of ring-down gravitational waves that are detectable by Advanced LIGO. Based on the SMBH formation history inferred from the evolution of the quasar luminosity function, we show that an observed event rate of 1 per year will constrain the SMBH mass fraction that was contributed by MBHs coalescence down to a level of ~10^-6 for 20 solar mass MBH remnants (or ~10^-4 for 260 solar mass remnants).Comment: 4 pages, 2 figures. Submitted to ApJ Letter

Asymptotic Quasinormal Frequencies of Different Spin Fields in Spherically Symmetric Black Holes

We consider the asymptotic quasinormal frequencies of various spin fields in Schwarzschild and Reissner-Nordstr\"om black holes. In the Schwarzschild case, the real part of the asymptotic frequency is ln3 for the spin 0 and the spin 2 fields, while for the spin 1/2, the spin 1, and the spin 3/2 fields it is zero. For the non-extreme charged black holes, the spin 3/2 Rarita-Schwinger field has the same asymptotic frequency as that of the integral spin fields. However, the asymptotic frequency of the Dirac field is different, and its real part is zero. For the extremal case, which is relevant to the supersymmetric consideration, all the spin fields have the same asymptotic frequency, the real part of which is zero. For the imaginary parts of the asymptotic frequencies, it is interesting to see that it has a universal spacing of $1/4M$ for all the spin fields in the single-horizon cases of the Schwarzschild and the extreme Reissner-Nordstr\"om black holes. The implications of these results to the universality of the asymptotic quasinormal frequencies are discussed.Comment: Revtex, 17 pages, 3 eps figures; one table, some remarks and references added to section I

Dirac Quasinormal modes of Schwarzschild black hole

The quasinormal modes (QNMs) associated with the decay of Dirac field perturbation around a Schwarzschild black hole is investigated by using continued fraction and Hill-determinant approaches. It is shown that the fundamental quasinormal frequencies become evenly spaced for large angular quantum number and the spacing is given by $\omega_{\lambda+1}- \omega_{\lambda}=0.38490-0.00000i$. The angular quantum number has the surprising effect of increasing real part of the quasinormal frequencies, but it almost does not affect imaginary part, especially for low overtones. In addition, the quasinormal frequencies also become evenly spaced for large overtone number and the spacing for imaginary part is $Im(\omega_{n+1})-Im(\omega_n)\approx -i/4M$ which is same as that of the scalar, electromagnetic, and gravitational perturbations.Comment: 14 pages, 5 figure

Late-Time Tails in Gravitational Collapse of a Self-Interacting (Massive) Scalar-Field and Decay of a Self-Interacting Scalar Hair

We study analytically the initial value problem for a self-interacting (massive) scalar-field on a Reissner-Nordstr\"om spacetime. Following the no-hair theorem we examine the dynamical physical mechanism by which the self-interacting (SI) hair decays. We show that the intermediate asymptotic behaviour of SI perturbations is dominated by an oscillatory inverse power-law decaying tail. We show that at late-times the decay of a SI hair is slower than any power-law. We confirm our analytical results by numerical simulations.Comment: 16 pages, 3 ps figures, Revte

The scalar perturbation of the higher-dimensional rotating black holes

The massless scalar field in the higher-dimensional Kerr black hole (Myers- Perry solution with a single rotation axis) has been investigated. It has been shown that the field equation is separable in arbitrary dimensions. The quasi-normal modes of the scalar field have been searched in five dimensions using the continued fraction method. The numerical result shows the evidence for the stability of the scalar perturbation of the five-dimensional Kerr black holes. The time scale of the resonant oscillation in the rapidly rotating black hole, in which case the horizon radius becomes small, is characterized by (black hole mass)^{1/2}(Planck mass)^{-3/2} rather than the light-crossing time of the horizon.Comment: 16 pages, 7 figures, revised versio

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

Quasinormal Ringing for Acoustic Black Holes at Low Temperature

We investigate a condensed matter ``black hole'' analogue, taking the Gross-Pitaevskii (GP) equation as a starting point. The linearized GP equation corresponds to a wave equation on a black hole background, giving quasinormal modes under some appropriate conditions. We suggest that we can know the detailed characters and corresponding geometrical information about the acoustic black hole by observing quasinormal ringdown waves in the low temperature condensed matters.Comment: 9 pages, 3 figures, PRD accepted versio

Massive scalar field quasi-normal modes of higher dimensional black holes

We study quasinormal spectrum of massive scalar field in the $D$-dimensional black hole background. We found the qualitatively different dependence on the field mass of the fundamental modes for $D\geq6$. The behaviour of higher modes is qualitatively the same for all $D$. Thus for some particular values of mass (of the field and of the black hole) the spectrum has two dominating oscillations with a very long lifetime. Also we show that the asymptotically high overtones do not depend on the field mass. In addition, we present the generalisation of the Nollert improvement of the continued fraction technique for the numerical calculation of quasi-normal frequencies of $D$-dimensional black holes.Comment: 8 pages, 4 figures, misprints corrected, version to appear in Phys. Rev.

Binary black hole merger dynamics and waveforms

We study dynamics and radiation generation in the last few orbits and merger of a binary black hole system, applying recently developed techniques for simulations of moving black holes. Our analysis of the gravitational radiation waveforms and dynamical black hole trajectories produces a consistent picture for a set of simulations with black holes beginning on circular-orbit trajectories at a variety of initial separations. We find profound agreement at the level of one percent among the simulations for the last orbit, merger and ringdown. We are confident that this part of our waveform result accurately represents the predictions from Einstein's General Relativity for the final burst of gravitational radiation resulting from the merger of an astrophysical system of equal-mass non-spinning black holes. The simulations result in a final black hole with spin parameter a/m=0.69. We also find good agreement at a level of roughly 10 percent for the radiation generated in the preceding few orbits.Comment: 11 pages, 11 figures, submitted to PRD, update citations, minor change