Quasi-Normal Modes for Subtracted Rotating and Magnetised Geometries

Abstract

We obtain explicit separable solutions of the wave equation of massless minimally coupled scalar fields in the subtracted geometry of four-dimensional rotating and Melvin (magnetised) four-charge black holes of the STU model, a consistent truncation of maximally supersymmetric supergravity with four types of electromagnetic fields. These backgrounds possess a hidden SL(2,R) x SL(2,R) x SO(3) symmetry and faithfully model the near horizon geometry of these black holes, but locate them in a confining asymptotically conical box. For each subtracted geometry we obtain two branches of quasi-normal modes, given in terms of hypergeometric functions and spherical harmonics. One branch is over-damped and the other under-damped and they exhibit rotational splitting. No black hole bomb is possible because the Killing field which co-rotates with the horizon is everywhere timelike outside the black hole. A five-dimensional lift of these geometries is given locally by the product of a BTZ black hole with a two-sphere. This allows an explicit analysis of the minimally coupled massive five-dimensional scalar field. Again, there are two branches, both damped, however now their oscillatory parts are shifted by the quantised wave number $k$ along the fifth circle direction.

28 pages minor corrections, added references

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Cited by in corpus (10)

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• Thermodynamics of Asymptotically Conical Geometries
• An Analysis of the Wave Equation for the $U(1{)}^2$ Gauged Supergravity Black Hole
• An analytical formula for the vacuum polarization of rotating black holes
• Scalar field quasinormal modes on asymptotically locally flat rotating black holes in three dimensions
• The Spectrum of Static Subtracted Geometries
• Exact scalar (quasi-)normal modes of black holes and solitons in gauged SUGRA