Classical and quantum temperature fluctuations via holography

TL;DR

This paper investigates temperature fluctuations in a 2+1D conformal field theory using holography, linking hydrodynamic modes to quantum and thermal fluctuations, and computes quasinormal modes numerically.

Contribution

It provides a numerical analysis of quasinormal frequencies for black holes in AdS and clarifies boundary conditions for low-lying modes in Reissner-Nordström black holes.

Findings

Determined quasinormal frequencies matching hydrodynamics at high temperature.

Identified boundary conditions for low-lying quasinormal modes in AdS black holes.

Linked temperature fluctuation spectra to hydrodynamic modes.

Abstract

We study local temperature fluctuations in a 2+1 dimensional CFT on the sphere, dual to a black hole in asymptotically AdS spacetime. The fluctuation spectrum is governed by the lowest-lying hydrodynamic modes of the system whose frequency and damping rate determine whether temperature fluctuations are thermal or quantum. We calculate numerically the corresponding quasinormal frequencies and match the result with the hydrodynamics of the dual CFT at large temperature. As a by-product of our analysis we determine the appropriate boundary conditions for calculating low-lying quasinormal modes for a four-dimensional Reissner-Nordstr\"om black hole in global AdS.