Abstract
We exploit the recently proposed correspondence between gravitational perturbations and quantum Seiberg-Witten curves to compute the spectrum of quasi-normal modes of asymptotically flat Kerr Newman black holes and establish detailed gauge/gravity dictionaries for a large class of black holes, D-branes and fuzzballs in diverse dimensions. QNM frequencies obtained from the quantum periods of SU(2) mathcal{N} = 2 SYM with Nf = 3 flavours are compared against numerical results, WKB (eikonal) approximation and geodetic motion showing remarkable agreement. Starting from the master example relating quasi-normal modes of Kerr-Newman black holes in AdS4 to SU(2) gauge theory with Nf = 4, we illustrate the procedure for some simple toy-models that allow analytic solutions. We also argue that the AGT version of the gauge/gravity correspondence may give precious hints as to the physical/geometric origin of the quasi-normal modes/Seiberg-Witten connection and further elucidate interesting properties (such as tidal Love numbers and grey-body factors) that can help discriminating black holes from fuzzballs.
Highlights
We argue that the AGT version of the gauge/gravity correspondence may give precious hints as to the physical/geometric origin of the quasi-normal modes/SeibergWitten connection and further elucidate interesting properties that can help discriminating black holes from fuzzballs
Compact gravitating objects, such as black holes (BHs), D-branes and micro-state geometries (‘fuzz-balls’) are often characterised by a set of Quasi-Normal Modes (QNMs) [1] that govern the linear response to external perturbations
In this subsection we consider near super-radiant modes, known as zero-damping modes (ZDMs), which are close to the super-radiant threshold frequency ωSR [69] and the imaginary part of the frequency is almost vanishing
Summary
Compact gravitating objects, such as black holes (BHs), D-branes and micro-state geometries (‘fuzz-balls’) are often characterised by a set of Quasi-Normal Modes (QNMs) [1] that govern the linear response to external perturbations. Quite recently, attempting exact WKB quantization techniques [20,21,22,23,24,25], a new astonishing gauge-gravity connection between the QNM spectral problem and quantum SeibergWitten (SW) curves [26,27,28] for N = 2 SYM theories was suggested and tested in the case of Kerr BHs in 4-d [29]. The QNM-SW correspondence was extended in [1] to several gravity systems including BHs in higher dimensions, D-branes, their bound-states and fuzzballs (smooth horizonless micro-state geometries). We relegate some technical details and some tables and plots of results to appendices A, B and C
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