Notes on Quasinormal Modes of charged de Sitter Blackholes from Quiver Gauge Theories

TL;DR

This paper derives connection formulae for differential equations from quiver gauge theories and uses them to analytically compute quasinormal modes of Reissner-Nordström de Sitter blackholes, validating results numerically.

Contribution

It introduces a novel method linking gauge theory data to differential equations for blackhole QNMs, providing explicit analytic expressions and numerical validation.

Findings

Analytic formulas for all QNM families including photon-sphere, dS, and near-extremal modes.

Numerical verification of the derived QNM spectra.

Potential extension of the method to dS-Kerr-Newman blackholes.

Abstract

We give the connection formulae for ordinary differential equations with 5 and 6 (and in principle can be generalized to more) regular singularities from the data of instanton partition functions of quiver gauge theories. We check the consistency of these connection formulae by numerically computing the quasinormal modes (QNMs) of Reissner-Nordstr\"om de Sitter (RN-dS) blackhole. Analytic expressions are obtained for all the families of QNMs, including the photon-sphere modes, dS modes, and near-extremal modes. We also argue that a similar method can be applied to the dS-Kerr-Newman blackhole.