Scalar, electromagnetic, and Weyl perturbations of BTZ black holes: Quasinormal modes

Abstract

We calculate the quasinormal modes and associated frequencies of the Bañados-Teitelboim-Zanelli ͑BTZ͒ nonrotating black hole. This black hole lives in 2ϩ1 dimensions in an asymptotically anti-de Sitter spacetime. We obtain exact results for the wave function and quasinormal frequencies of scalar, electromagnetic and Weyl ͑neutrino͒ perturbations.

Black hole collision with a scalar particle in four-, five-, and seven-dimensional anti–de Sitter spacetimes: Ringing and radiation

“…10, 11 and 13), as it did in flat spacetime [24]. (Scalar quasinormal frequencies of Schwarzschild-AdS black holes can be found in [4,6]). Most importantly, the location of the peak seems to have a strong dependence on r 0 (compare Figs.…”

“…4-7 are typical plots for small black holes of waveforms and spectra for l = 0 and l = 1 (for l = 2 and higher the conclusions are not altered). They show the first interesting aspect of our numerical results: for small black holes the l = 0 signal is clearly dominated by quasinormal, exponentially decaying, ringing modes with a frequency ω ∼ d − 1 (scalar quasinormal frequencies of Schwarzschild-AdS black holes can be found in [4,6]). This particular limit is a pure AdS mode [20,21].…”

“…¿From the point of view of the AdS/CFT conjecture, where the (large) black hole corresponds on the CFT side to a thermal state, the infalling scalar particle corresponds to a specific perturbation of this state (an expanding bubble), while the scalar radiation is interpreted as particles decaying into bosons of the associated operator of the gauge theory. Previous works [4,6] have shown that a general perturbation should have a timescale directly related to the inverse of the imaginary part of the quasinormal frequency, which means that the approach to thermal equilibrium on the CFT should be governed by this timescale. We have shown through a specific important problem that this is in fact correct, but that it is not the whole story, since some important features of the waveforms highly depend on r 0 .…”

Classical super-radiance in Kerr–Newman–anti-de Sitter black holes

“…Further, the potentialṼ ωlm diverges at infinity unless µ 2 = −2/l 2 . Some studies of the quasi-normal modes on asymptotically antide Sitter black holes (see, for example, [39,40,41,42,43,44]) have considered massless, minimally coupled scalar fields, for whichμ = 0. Therefore, in that case, the potential is divergent at infinity and the boundary conditioñ F ωlm → 0 as r * → r * ∞ was employed.…”

Investigating Brane Resolution with Perturbative Dynamics

“…Thus, by restricting ourselves to solutions of purely real ω we may be missing some interesting dynamical features. In this vein, we compute exactly the quasinormal modes [16,17]. For large ρ, the wave function solution (4.3) is…”