Shijun Yoshida

Highly damped quasinormal modes of Kerr black holes: A complete numerical investigation

We compute for the first time very highly damped quasinormal modes of the (rotating) Kerr black hole. Our numerical technique is based on a decoupling of the radial and angular equations, performed using a large-frequency expansion for the angular separation constant_{s}A_{l m}. This allows us to go much further in overtone number than ever before. We find that the real part of the quasinormal frequencies approaches a non-zero constant value which does not depend on the spin s of the perturbing field and on the angular index l: \omega_R=m\varpi(a). We numerically compute \varpi(a). Leading-order corrections to the asymptotic frequency are likely to be of order 1/\omega_I. The imaginary part grows without bound, the spacing between consecutive modes being a monotonic function of a.

Quasinormal modes of Schwarzschild black holes in four-dimensions and higher dimensions

We make a thorough investigation of the asymptotic quasinormal modes of the four and five-dimensional Schwarzschild black hole for scalar, electromagnetic and gravitational perturbations. Our numerical results give full support to all the analytical predictions by Motl and Neitzke, for the leading term. We also compute the first order corrections analytically, by extending to higher dimensions, previous work of Musiri and Siopsis, and find excellent agreement with the numerical results. For generic spacetime dimension number D the first-order corrections go as

Classical instability of Kerr-AdS black holes and the issue of final state

\frac{1}{n^{(D-3)/(D-2)}}

Equilibrium Configurations of Magnetized Rotating Polytropes: Effects of Strong Toroidal Magnetic Fields in Addition to Poloidal Magnetic Fields

. This means that there is a more rapid convergence to the asymptotic value for the five dimensional case than for the four dimensional case, as we also show numerically.

Relativistic stars with purely toroidal magnetic fields

It is now established that small Kerr\char21{}anti-de Sitter (Kerr-AdS) black holes are unstable against scalar perturbations, via the superradiant amplification mechanism. We show that small Kerr-AdS black holes are also unstable against gravitational perturbations and we compute the features of this instability. We also describe with great detail the evolution of this instability. In particular, we identify its end-point state. It corresponds to a Kerr-AdS black hole whose boundary is an Einstein universe rotating with the light velocity. This black hole is expected to be slightly oblate and to coexist in equilibrium with a certain amount of outside radiation.

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

We have constructed many equilibrium sequences of magnetized polytropic stars with infinite conductivity for polytropes of indices N = 0.5, 1, and 3. Not only poloidal magnetic fields but also toroidal magnetic fields have been included in addition to rotation. By choosing simplified forms for arbitrary functions appearing in the formulation of magnetized barotropic equilibrium stars, we have obtained strongly magnetized polytropes whose toroidal magnetic fields are of comparable strength to those of poloidal magnetic fields. The exterior magnetic fields of the obtained stars consist of dipole-like poloidal fields, which decrease as r-3 when r → ∞. On the other hand, the interior magnetic fields are mixed poloidal-toroidal, which are composed of tori of twisted field lines around the symmetry axis and of untwisted poloidal fields that continue to the exterior fields penetrating the surfaces of the stars.

Accuracy of the relativistic Cowling approximation in slowly rotating stars

We investigate the effects of the purely toroidal magnetic field on the equilibrium structures of the relativistic stars. The basic equations for obtaining equilibrium solutions of relativistic rotating stars containing purely toroidal magnetic fields are derived for the first time. To solve these basic equations numerically, we extend the Cook-Shapiro-Teukolsky scheme for calculating relativistic rotating stars containing no magnetic field to incorporate the effects of the purely toroidal magnetic fields. By using the numerical scheme, we then calculate a large number of the equilibrium configurations for a particular distribution of the magnetic field in order to explore the equilibrium properties. We also construct the equilibrium sequences of the constant baryon mass and/or the constant magnetic flux, which model the evolution of an isolated neutron star as it loses angular momentum via the gravitational waves. Important properties of the equilibrium configurations of the magnetized stars obtained in this study are summarized as follows: (1) For the nonrotating stars, the matter distribution of the stars is prolately distorted due to the toroidal magnetic fields. (2) For the rapidly rotating stars, the shape of the stellar surface becomes oblate because of the centrifugal force. But, the matter distribution deep inside the star is sufficiently prolate for the mean matter distribution of the star to be prolate. (3) The stronger toroidal magnetic fields lead to the mass shedding of the stars at the lower angular velocity. (4) For some equilibrium sequences of the constant baryon mass and magnetic flux, the stars can spin up as they lose angular momentum.

Late time tails of wave propagation in higher dimensional space-times

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 nonlinear 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.

SEARCH FOR EXTRATERRESTRIAL ANTINEUTRINO SOURCES WITH THE KamLAND DETECTOR

We have calculated the non-radial oscillation in slowly rotating relativistic stars with the Cowling approximation. The frequencies are compared with those based on the complete linearized equations of general relativity. It is found that the results with the approximation differ by less than about

r-Modes of Neutron Stars with a Solid Crust

20 %