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

Quasinormal Modes of Kerr Black Holes in Four and Higher Dimensions

We analytically calculate to leading order the asymptotic form of quasinormal frequencies of Kerr black holes in four, five and seven dimensions. All the relevant quantities can be explicitly expressed in terms of elliptical integrals. In four dimensions, we confirm the results obtained by Keshest and Hod by comparing the analytic results to the numerical ones.Comment: 14 pages, 7 figure

Quasinormal modes of black holes localized on the Randall-Sundrum 2-brane

We investigate conformal scalar, electromagnetic, and massless Dirac quasinormal modes of a brane-localized black hole. The background solution is the four-dimensional black hole on a 2-brane that has been constructed by Emparan, Horowitz, and Myers in the context of a lower dimensional version of the Randall-Sundrum model. The conformally transformed metric admits a Killing tensor, allowing us to obtain separable field equations. We find that the radial equations take the same form as in the four-dimensional "braneless" Schwarzschild black hole. The angular equations are, however, different from the standard ones, leading to a different prediction for quasinormal frequencies.Comment: 10 pages, 7 figures; references added, version to appear in PR

Exact Gravitational Quasinormal Frequencies of Topological Black Holes

We compute the exact gravitational quasinormal frequencies for massless topological black holes in d-dimensional anti-de Sitter space. Using the gauge invariant formalism for gravitational perturbations derived by Kodama and Ishibashi, we show that in all cases the scalar, vector, and tensor modes can be reduced to a simple scalar field equation. This equation is exactly solvable in terms of hypergeometric functions, thus allowing an exact analytic determination of the gravitational quasinormal frequencies.Comment: 14 pages, Latex; v2 additional reference

Quasinormal modes of the charged black hole in Gauss-Bonnet gravity

The d-dimensional string generated gravity models lead to Einstein-Maxwell equations with quadratic order correction term called the Gauss-Bonnet term. We calculate the quasinormal modes for the d-dimensional charged black hole in the framework of this model. The quasinormal spectrum essentially depends upon the Gauss-Bonnet coupling parameter $\alpha$ which is related to the string scale, and is totally different from that for black holes derived from Einstein action. In particular, at large $\alpha$ the quasinormal modes are proportional to $\alpha$, while as $\alpha$ goes to zero the qusinormal modes approach their Schwarzschild values. In contrary to Einstein theory black hole behavior, the damping rate of the charged GB black hole as a function of charge does not contain a chracteristic maximum, but instead the monotonic falling down is observed. In addition, there have been obtained an asymptotic formula for large multipole numbers.Comment: 16 pages, 4 figures, 3 tables; misprints correcte

Continuous area spectrum in regular black hole

We investigate highly damped quasinormal modes of regular black hole coupled to nonlinear electrodynamics. Using the WKB approximation combined with complex-integration technique, we show that the real part of the frequency disappears in the highly damped limit. If we use the Bohr's correspondence principle, the area spectrum of this black hole is continuous. We discuss its implication in the loop quantum gravity.Comment: 5 pages, 1 figure

Dynamical evolution of a scalar field coupling to Einstein's tensor in the Reissner-Nordstr\"{o}m black hole spacetime

We study the dynamical evolution of a scalar field coupling to Einstein's tensor in the background of Reissner-Nordstr\"{o}m black hole. Our results show that the the coupling constant $\eta$ imprints in the wave dynamics of a scalar perturbation. In the weak coupling, we find that with the increase of the coupling constant $\eta$ the real parts of the fundamental quasinormal frequencies decrease and the absolute values of imaginary parts increase for fixed charge $q$ and multipole number $l$. In the strong coupling, we find that for $l\neq0$ the instability occurs when $\eta$ is larger than a certain threshold value $\eta_c$ which deceases with the multipole number $l$ and charge $q$. However, for the lowest $l=0$, we find that there does not exist such a threshold value and the scalar field always decays for arbitrary coupling constant.Comment: 11 pages, 6 figures, accepted for publication in Phys Rev

PP-Wave / CFT_2 Duality

We investigate the pp-wave limit of the AdS_3\times S^3\times K3 compactification of Type IIB string theory from the point of view of the dual Sym_N(K3) CFT. It is proposed that a fundamental string in this pp-wave geometry is dual to the c=6 effective string of the Sym_N(K3) CFT, with the string bits of the latter being composed of twist operators. The massive fundamental string oscillators correspond to certain twisted Virasoro generators in the effective string. It is shown that both the ground states and the genus expansion parameter (at least in the orbifold limit of the CFT) coincide. Surprisingly the latter scales like J^2/N rather than the J^4/N^2 which might have been expected. We demonstrate a leading-order agreement between the pp-wave and CFT particle spectra. For a degenerate special case (one NS 5-brane) an intriguing complete agreement is found.Comment: JHEP3 LaTeX, 20 pages; discussion of WZW levels clarified, reference adde

A Universal Temperature Profile for Galaxy Clusters

We investigate the predicted present-day temperature profiles of the hot, X-ray emitting gas in galaxy clusters for two cosmological models - a current best-guess LCDM model and standard cold dark matter (SCDM). Our numerically-simulated "catalogs" of clusters are derived from high-resolution (15/h kpc) simulations which make use of a sophisticated, Eulerian-based, Adaptive Mesh-Refinement (AMR) code that faithfully captures the shocks which are essential for correctly modelling cluster temperatures. We show that the temperature structure on Mpc-scales is highly complex and non-isothermal. However, the temperature profiles of the simulated LCDM and SCDM clusters are remarkably similar and drop-off as $T +AFw-propto (1+-r/a_x)^{-+AFw-delta}$ where $a_x +AFw-sim r_{vir}/1.5$ and $+AFw-delta +AFw-sim 1.6$. This decrease is in good agreement with the observational results of Markevitch et al.(1998) but diverges, primarily in the innermost regions, from their fit which assumes a polytropic equation of state. Our result is also in good agreement with a recent sample of clusters observed by BeppoSAX though there is some indication of missing physics at small radii ($r<0.2 r_{vir}$). We discuss the interpretation of our results and make predictions for new x-ray observations that will extend to larger radii than previously possible. Finally, we show that, for $r>0.2 r_{vir}$, our universal temperature profile is consistent with our most recent simulations which include both radiative cooling and supernovae feedback.Comment: 8 pages, 6 figures, accepted for publication in ApJ, full-page version of Fig. 2 at http://www.cita.utoronto.ca/+AH4-cloken/PAPERS/UTP/f2.ep