Perturbative Calculation of Quasinormal Modes of $d$--Dimensional Black Holes

Abstract

We study analytically quasinormal modes in a wide variety of black hole spacetimes, including $d$--dimensional asymptotically flat spacetimes and non-asymptotically flat spacetimes (particular attention has been paid to the four dimensional case). We extend the analytical calculation to include first-order corrections to analytical expressions for quasinormal mode frequencies by making use of a monodromy technique. All possible type perturbations are included in this paper. The calculation performed in this paper show that systematic expansions for uncharged black holes include different corrections with the ones for charged black holes. This difference makes them have a different $n$--dependence relation in the first-order correction formulae. The method applied above in calculating the first-order corrections of quasinormal mode frequencies seems to be unavailable for black holes with small charge. This result supports the Neitzke's prediction. On what concerns quantum gravity we confirm the view that the $\ln 3$ in $d=4$ Schwarzschild seems to be nothing but some numerical coincidences.

49 pages, 5 figures

References in corpus (3)

• WKB analysis of the Regge-Wheeler equation down in the frequency plane
• Greybody factors at large imaginary frequencies
• The Highly Damped Quasinormal Modes of $d$-dimensional Reissner-Nordstrom Black Holes in the Small Charge Limit

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• Looking at the Gregory-Laflamme instability through quasi-normal modes
• Electromagnetic quasinormal modes of D-dimensional black holes II
• On black holes with scalar hairs
• Generic master equations for quasi-normal frequencies
• Second Order Perturbative Calculation of Quasinormal Modes of Schwarzschild Black Holes
• Riemann-Christoffel flows