On the classification of asymptotic quasinormal frequencies for $d$-dimensional black holes and quantum gravity
By José Natário, R. Schiappa. 2004
206 citations recorded by the source corpus.
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–Nordstrom are dimension dependent (the extremal Reissner–Nordstrom 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–Nordstrom de Sitter there is a dimension dependent formula for the frequencies, except in dimension d = 5 where the formula is different. Schwarzschild and Reissner–Nordstrom 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 spacetime—where 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.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/d3e5d8bf24b0704992e6bda58924f4a2ba368434
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Citations in the corpus
- Overdamped modes in Schwarzschild-de Sitter and a Mathematica package for the numerical computation of quasinormal modes (2017, background): “While there are some cases where it can be done analytically (a recent quite involved example is [21], and see [22] for a review of analytic computations and approximations), of course the generic case can only be done numerically.”
- Frequency-dependent effects of gravitational lensing within plasma (2015, background): “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).”
- Static patch solipsism: conformal symmetry of the de Sitter worldline (2011, background): “The resulting Schrödinger potentials, for scalar, vector and tensor modes respectively, are [38, 39]”
- Quantum oscillations and black hole ringing (2009, methodology): “The integral in (98) is along the Stokes line specified in [53].”
- Black hole determinants and quasinormal modes (2009, unknown): “Examples of such computations include [47, 48, 49, 50, 51].”
- Holographic thermalization, quasinormal modes and superradiance in Kerr-AdS (2013, methodology): “The associated QNMs of the global AdS Schwarzchild BH were then computed [9, 10, 30]: vector QNMs agree with those first computed in [31, 32, 33] (the scalar modes of [31, 32, 33] do not preserve the asymptotic AdS structure).”
- A primer on resurgent transseries and their asymptotics (2018, background): “, [190, 193, 57, 192, 143]) and, in fact, it would be very interesting to further apply resurgent analysis to this large class of gravitational problems.”