Gravitational instability of simply rotating AdS black holes in higher dimensions

We study the stability of AdS black hole holes rotating in a single two plane for tensor-type gravitational perturbations in $D > 6$ space-time dimensions. First, by an analytic method, we show that there exists no unstable mode when the magnitude $a$ of the angular momentum is smaller than $r_h^2/R$ where $r_h$ is the horizon radius, and $R$ is the AdS curvature radius. Then, by numerical calculations of quasinormal modes, using the separability of the relevant perturbation equations, we show that an instability occurs for rapidly rotating black holes with $a>r_h^2/R$, although the growth rate is tiny (of order $10^{-12}$ of the inverse horizon radius). We give numerical evidences indicating that this instability is caused by superradiance.Comment: 17 page

Quasi-Normal Modes of Brane-Localised Standard Model Fields II: Kerr Black Holes

This paper presents a comprehensive study of the fundamental quasinormal modes of all Standard Model fields propagating on a brane embedded in a higher-dimensional rotating black hole spacetime. The equations of motion for fields with spin $s=0, 1/2$ and 1 propagating in the induced-on-the-brane background are solved numerically, and the dependence of their QN spectra on the black hole angular momentum and dimensionality of spacetime is investigated. It is found that the brane-localised field perturbations are longer-lived when the higher-dimensional black hole rotates faster, while an increase in the number of transverse-to-the-brane dimensions reduces their lifetime. Finally, the quality factor $Q$, that determines the best oscillator among the different field perturbations, is investigated and found to depend on properties of both the particular field studied (spin, multipole numbers) and the gravitational background (dimensionality, black hole angular momentum number).Comment: 12 pages, 8 figures, typos corrected, version to appear in Phys. Rev.

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.

Universality of Highly Damped Quasinormal Modes for Single Horizon Black Holes

It has been suggested that the highly damped quasinormal modes of black holes provide information about the microscopic quantum gravitational states underlying black hole entropy. This interpretation requires the form of the highly damped quasinormal mode frequency to be universally of the form: $\hbar\omega_R = \ln(l)kT_{BH}$, where $l$ is an integer, and $T_{BH}$ is the black hole temperature. We summarize the results of an analysis of the highly damped quasinormal modes for a large class of single horizon, asymptotically flat black holes.Comment: 9 pages, 1 figure, submitted to the proceedings of Theory CANADA 1, which will be published in a special edition of the Canadian Journal of Physic

Quantum oscillations and black hole ringing

We show that strongly coupled field theories with holographic gravity duals at finite charge density and low temperatures can undergo de Haas - van Alphen quantum oscillations as a function of an external magnetic field. Exhibiting this effect requires computation of the one loop contribution of charged bulk fermions to the free energy. The one loop calculation is performed using a formula expressing determinants in black hole backgrounds as sums over quasinormal modes. At zero temperature, the periodic nonanalyticities in the magnetic susceptibility as a function of the inverse magnetic field depend on the low energy scaling behavior of fermionic operators in the field theory, and are found to be softer than in weakly coupled theories. We also obtain numerical and WKB results for the quasinormal modes of charged bosons in dyonic black hole backgrounds, finding evidence for nontrivial periodic behavior as a function of the magnetic field.Comment: 1+53 pages. 9 figures. v2: important changes to sections 3.4 - 3.6. contribution of branch cut poles include

Quasi-normal modes, area spectra and multi-horizon spacetimes

We suggest an interpretation for the highly damped QNM frequencies of the spherically symmetric multi-horizon spacetimes (Reissner-Nordstrom, Schwarzschild-deSitter, Reissner-Nordstrom-deSitter) following Maggiore's proposal about the link between the asymptotic QNM frequencies and the black hole thermodynamics. We show that the behavior of the asymptotic frequencies is easy to understand if one assumes that all of the horizons have the same equispaced area spectra. The QNM analysis is then consistent with the choice of the area spectra to be the one originally proposed for the black hole's horizon by Bekenstein: A=8\pi n (in Planck units). The interpretation of the highly damped QNM frequencies in the multi-horizon case is based on the similar grounds as in the single horizon (Schwarzschild) case, but it has some new features that are discussed in the paper.Comment: 8 pages, v2: no physics changed, some references added, few sentences added in the discussion part

The phase transition and the Quasi-Normal Modes of black Holes

We reexamined the argument that the quasinormal modes could be a probe of the phase transition of a topological black hole to a hairy configuration by investigating general scalar perturbations. We found further evidence in the quasinormal modes for this phase transition. For the general black hole configurations, we observed that although the quasinormal modes can present us different phases of different configurations, there is no dramatic change in the slope of quasinormal frequencies at the critical point of the phase transition. More detailed studies of quasinormal modes are needed to reveal the subtle behavior of the phase transition.Comment: Revised version, accepted for publication in JHE

Asymptotic quasinormal modes of scalar field in a gravity's rainbow

In the context of a gravity's rainbow, the asymptotic quasinormal modes of the scalar perturbation in the quantum modified Schwarzschild black holes are investigated. By using the monodromy method, we calculated and obtained the asymptotic quasinormal frequencies, which are dominated not only by the mass parameter of the spacetime, but also by the energy functions from the modified dispersion relations. However, the real parts of the asymptotic quasinormal modes is still $T_H\ln 3$, which is consistent with Hod's conjecture. In addition, for the quantum corrected black hole, the area spacing is calculated and the result is independent of the energy functions, in spite of the area itself is energy dependence. And that, by relating the area spectrum to loop quantum gravity, the Barbero-Immirzi parameter is given and it remains the same as from the usual black hole

Quasi-normal Modes of Electromagnetic Perturbations of Four-Dimensional Topological Black Holes with Scalar Hair

We study the perturbative behaviour of topological black holes with scalar hair. We calculate both analytically and numerically the quasi-normal modes of the electromagnetic perturbations. In the case of small black holes we find evidence of a second-order phase transition of a topological black hole to a hairy configuration.Comment: v2: 19 pages, 2 figures, added references, improved discussion, to appear in JHE

Area spectra of the rotating BTZ black hole from quasinormal modes

Following Bekenstein's suggestion that the horizon area of a black hole should be quantized, the discrete spectrum of the horizon area has been investigated in various ways. By considering the quasinormal mode of a black hole, we obtain the transition frequency of the black hole, analogous to the case of a hydrogen atom, in the semiclassical limit. According to Bohr's correspondence principle, this transition frequency at large quantum number is equal to classical oscillation frequency. For the corresponding classical system of periodic motion with this oscillation frequency, an action variable is identified and quantized via Bohr-Sommerfeld quantization, from which the quantized spectrum of the horizon area is obtained. This method can be applied for black holes with discrete quasinormal modes. As an example, we apply the method for the both non-rotating and rotating BTZ black holes and obtain that the spectrum of the horizon area is equally spaced and independent of the cosmological constant for both cases