Continuous phase transition in polydisperse hard-sphere mixture

In a previous paper (J. Zhang {\it et al.}, J. Chem. Phys. {\bf 110}, 5318 (1999)) we introduced a model for polydisperse hard sphere mixtures that is able to adjust its particle-size distribution. Here we give the explanation of the questions that arose in the previous description and present a consistent theory of the phase transition in this system, based on the Percus-Yevick equation of state. The transition is continuous, and like Bose-Einstein condensation a macroscopic aggregate is formed due to the microscopic interactions. A BMCSL-like treatment leads to the same conclusion with slightly more accurate predictions.Comment: 7 pages including 5 figures in revte

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

A detailed study of quasinormal frequencies of the Kerr black hole

We compute the quasinormal frequencies of the Kerr black hole using a continued fraction method. The continued fraction method first proposed by Leaver is still the only known method stable and accurate for the numerical determination of the Kerr quasinormal frequencies. We numerically obtain not only the slowly but also the rapidly damped quasinormal frequencies and analyze the peculiar behavior of these frequencies at the Kerr limit. We also calculate the algebraically special frequency first identified by Chandrasekhar and confirm that it coincide with the $n=8$ quasinormal frequency only at the Schwarzschild limit.Comment: REVTEX, 15 pages, 7 eps figure

On the Maximum Mass of Differentially Rotating Neutron Stars

We construct relativistic equilibrium models of differentially rotating neutron stars and show that they can support significantly more mass than their nonrotating or uniformly rotating counterparts. We dynamically evolve such ``hypermassive'' models in full general relativity and show that there do exist configurations which are dynamically stable against radial collapse and bar formation. Our results suggest that the remnant of binary neutron star coalescence may be temporarily stabilized by differential rotation, leading to delayed collapse and a delayed gravitational wave burst.Comment: 4 pages, 2 figures, uses emulateapj.sty; to appear in ApJ Letter

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

Possible direct method to determine the radius of a star from the spectrum of gravitational wave signals

We computed the spectrum of gravitational waves from a dust disk star of radius R inspiraling into a Kerr black hole of mass M and specific angular momentum a. We found that when R is much larger than the wave length of the quasinormal mode, the spectrum has several peaks and the separation of peaks $\Delta\omega$ is proportional to $R^{-1}$ irrespective of M and a. This suggests that the radius of the star in coalescing binary black hole - star systems may be determined directly from the observed spectrum of gravitational wave. This also suggests that the spectrum of the radiation may give us important information in gravitational wave astronomy as in optical astronomy.Comment: 4 pages with 3 eps figures, revtex.sty, accepted for publication in Phys. Rev. Let

Quasinormal ringing of Kerr black holes: The excitation factors

Distorted black holes radiate gravitational waves. In the so-called ringdown phase radiation is emitted in a discrete set of complex quasinormal frequencies, whose values depend only on the black hole's mass and angular momentum. Ringdown radiation could be detectable with large signal-to-noise ratio by the Laser Interferometer Space Antenna LISA. If more than one mode is detected, tests of the black hole nature of the source become possible. The detectability of different modes depends on their relative excitation, which in turn depends on the cause of the perturbation (i.e. on the initial data). A ``universal'', initial data-independent measure of the relative mode excitation is encoded in the poles of the Green's function that propagates small perturbations of the geometry (``excitation factors''). We compute for the first time the excitation factors for general-spin perturbations of Kerr black holes. We find that for corotating modes with $l=m$ the excitation factors tend to zero in the extremal limit, and that the contribution of the overtones should be more significant when the black hole is fast rotating. We also present the first analytical calculation of the large-damping asymptotics of the excitation factors for static black holes, including the Schwarzschild and Reissner-Nordstrom metrics. This is an important step to determine the convergence properties of the quasinormal mode expansion.Comment: 33 pages, 9 figures, 7 tables, RevTeX4. v2: Two new figures and minor changes in the presentation. Matches version in press in Phys. Rev.

Asymptotic power-law tails of massive scalar fields in Reissner-Nordstr\"{o}m background

We investigate dominant late-time tail behaviors of massive scalar fields in nearly extreme Reissner-Nordstr\"{o}m background. It is shown that the oscillatory tail of the scalar fields has the decay rate of $t^{-5/6}$ at asymptotically late times. The physical mechanism by which the asymptotic $t^{-5/6}$ tail yields and the relation between the field mass and the time scale when the tail begins to dominate, are discussed in terms of resonance backscattering due to spacetime curvature.Comment: 18 pages, 1 figure, accepted for publication in Physical Review

Asymptotic tails of massive scalar fields in a stationary axisymmetric EMDA black hole geometry

The late-time tail behavior of massive scalar fields is studied analytically in a stationary axisymmetric EMDA black hole geometry. It is shown that the asymptotic behavior of massive perturbations is dominated by the oscillatory inverse power-law decaying tail $t^{-(l+3/2)}\sin(\mu t)$ at the intermediate late times, and by the asymptotic tail $t^{-5/6}\sin(\mu t)$ at asymptotically late times. Our result seems to suggest that the intermediate tails $t^{-(l+3/2)}\sin(\mu t)$ and the asymptotically tails $t^{-5/6} \sin(\mu t)$ may be quite general features for evolution of massive scalar fields in any four dimensional asymptotically flat rotating black hole backgrounds.Comment: 6 page

Superradiant instabilities of rotating black branes and strings

Black branes and strings are generally unstable against a certain sector of gravitational perturbations. This is known as the Gregory-Laflamme instability. It has been recently argued that there exists another general instability affecting many rotating extended black objects. This instability is in a sense universal, in that it is triggered by any massless field, and not just gravitational perturbations. Here we investigate this novel mechanism in detail. For this instability to work, two ingredients are necessary: (i) an ergo-region, which gives rise to superradiant amplification of waves, and (ii) ``bound'' states in the effective potential governing the evolution of the particular mode under study. We show that the black brane Kerr_4 x R^p is unstable against this mechanism, and we present numerical results for instability timescales for this case. On the other hand, and quite surprisingly, black branes of the form Kerr_d x R^p are all stable against this mechanism for d>4. This is quite an unexpected result, and it stems from the fact that there are no stable circular orbits in higher dimensional black hole spacetimes, or in a wave picture, that there are no bound states in the effective potential. We also show that it is quite easy to simulate this instability in the laboratory with acoustic black branes.Comment: 19 pages, 10 figures. v2: Enlarged discussion on the necessary conditions for the existence of instabilit