On the classification of asymptotic quasinormal frequencies for {$d$}-dimensional black holes and quantum gravity

Abstract

We provide a complete classification of asymptotic quasinormal frequencies for static, spherically symmetric black hole spacetimes in d dimensions. This includes all possible types of gravitational perturbations (tensor, vector and scalar type) as described by the Ishibashi-Kodama master equations. The frequencies for Schwarzschild are dimension independent, while for Reissner-Nordström are dimension dependent (the extremal Reissner-Nordström case must be considered separately from the non-extremal case). For Schwarzschild de Sitter, there is a dimension independent formula for the frequencies, except in dimension d = 5 where the formula is different. For Reissner-Nordström de Sitter there is a dimension dependent formula for the frequencies, except in dimension d = 5 where the formula is different. Schwarzschild and Reissner-Nordström Anti-de Sitter black hole spacetimes are simpler: the formulae for the frequencies will depend upon a parameter related to the tortoise coordinate at spatial infinity, and scalar type perturbations in dimension d = 5 lead to a continuous spectrum for the quasinormal frequencies. We also address non-black hole spacetimes, such as pure de Sitter spacetimewhere there are quasinormal modes only in odd dimensions-and pure Anti-de Sitter spacetime-where again scalar type perturbations in dimension d = 5 lead to a continuous spectrum for the normal frequencies. Our results match previous numerical calculations with great accuracy. Asymptotic quasinormal frequencies have also been applied in the framework of quantum gravity for black holes. Our results show that it is only in the simple Schwarzschild case which is possible to obtain sensible results concerning area quantization or loop quantum gravity. In an effort to keep this paper self-contained we also review earlier results in the literature.

Split fermion quasinormal modes

“…Note that these results are in accordance with that of integral spin fields in higher-dimensional Schwarzschild spacetimes [20,21,22].…”

Frequency-dependent effects of gravitational lensing within plasma

“…Introducing terms into the effective potential through refractive plasma brings new behaviour to the trajectories of light rays, some of which correspond analogously to known cases. For example, the h = 3 case is related to the effective potential found in the Klein-Gordon equation that describes the evolution of scalar field perturbations on the Schwarzschild space-time (Chandrasekhar & Detweiller 1975;Natario & Schiappa 2004;Skakala & Visser 2010). To proceed, we assume the energy density of the scalar field to be small and its influence on the space-time geometry negligible.…”

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

“…The asymptotic QNMs (n ≫ 1) are obtained using the monodromy method [36,37,38,39,40] (see [41,42,43] for numerical calculations and [44] for the other method). For a (conformal) scalar field in the Schwarzschild background, we have…”