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

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

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

High overtones of Dirac perturbations of a Schwarzschild black hole

Using the Frobenius method, we find high overtones of the Dirac quasinormal spectrum for the Schwarzschild black hole. At high overtones, the spacing for imaginary part of $\omega_{n}$ is equidistant and equals to $\Im{\omega_{n+1}}-\Im{\omega_{n}} =i/8M$, ($M$ is the black hole mass), which is twice less than that for fields of integer spin. At high overtones, the real part of $\omega_{n}$ goes to zero. This supports the suggestion that the expected correspondence between quasinormal modes and Barbero-Immirzi parameter in Loop Quantum Gravity is just a numerical coincidence.Comment: 5 pages, Latex, 3 figures, Physical Review D.,at pres

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

Scalar field evolution in Gauss-Bonnet black holes

It is presented a thorough analysis of scalar perturbations in the background of Gauss-Bonnet, Gauss-Bonnet-de Sitter and Gauss-Bonnet-anti-de Sitter black hole spacetimes. The perturbations are considered both in frequency and time domain. The dependence of the scalar field evolution on the values of the cosmological constant $\Lambda$ and the Gauss-Bonnet coupling $\alpha$ is investigated. For Gauss-Bonnet and Gauss-Bonnet-de Sitter black holes, at asymptotically late times either power-law or exponential tails dominate, while for Gauss-Bonnet-anti-de Sitter black hole, the quasinormal modes govern the scalar field decay at all times. The power-law tails at asymptotically late times for odd-dimensional Gauss-Bonnet black holes does not depend on $\alpha$, even though the black hole metric contains $\alpha$ as a new parameter. The corrections to quasinormal spectrum due to Gauss-Bonnet coupling is not small and should not be neglected. For the limit of near extremal value of the (positive) cosmological constant and pure de Sitter and anti-de Sitter modes in Gauss-Bonnet gravity we have found analytical expressions.Comment: 10 pages, to be published in Phys. Rev.

Non-Quasinormal Modes and Black Hole Physics

The near-horizon geometry of a large class of extremal and near-extremal black holes in string and M theory contains three-dimensional asymptotically anti-de Sitter space. Motivated by this structure, we are led naturally to a discrete set of complex frequencies defined in terms of the monodromy at the inner and outer horizons of the black hole. We show that the correspondence principle, whereby the real part of these ``non-quasinormal frequencies'' is identified with certain fundamental quanta, leads directly to the correct quantum behavior of the near-horizon Virasoro algebra, and thus the black hole entropy. Remarkably, for the rotating black hole in five dimensions we also reproduce the fractionization of conformal weights predicted in string theory.Comment: 4 pages, revtex4; v2: reference added; v3: more references, minor typo corrected; v4: minor rewording to adjust size (ugh!); v5: some small clarifications at referees' suggestio

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.

The Mystery of the Asymptotic Quasinormal Modes of Gauss-Bonnet Black Holes

We analyze the quasinormal modes of $D$-dimensional Schwarzschild black holes with the Gauss-Bonnet correction in the large damping limit and show that standard analytic techniques cannot be applied in a straightforward manner to the case of infinite damping. However, by using a combination of analytic and numeric techniques we are able to calculate the quasinormal mode frequencies in a range where the damping is large but finite. We show that for this damping region the famous $\ln(3)$ appears in the real part of the quasinormal mode frequency. In our calculations, the Gauss-Bonnet coupling, $\alpha$, is taken to be much smaller than the parameter $\mu$, which is related to the black hole mass.Comment: 12 pages and 5 figure

Resonant excitations of the 't Hooft-Polyakov monopole

The spherically symmetric magnetic monopole in an SU(2) gauge theory coupled to a massless Higgs field is shown to possess an infinite number of resonances or quasinormal modes. These modes are eigenfunctions of the isospin 1 perturbation equations with complex eigenvalues, $E_n=\omega_n-i\gamma_n$, satisfying the outgoing radiation condition. For $n\to\infty$, their frequencies $\omega_n$ approach the mass of the vector boson, $M_W$, while their lifetimes $1/\gamma_n$ tend to infinity. The response of the monopole to an arbitrary initial perturbation is largely determined by these resonant modes, whose collective effect leads to the formation of a long living breather-like excitation characterized by pulsations with a frequency approaching $M_W$ and with an amplitude decaying at late times as $t^{-5/6}$.Comment: 4 page