Dyonic AdS black holes from magnetohydrodynamics

TL;DR

This paper explores the duality between large dyonic AdS black holes and relativistic magnetohydrodynamics, providing new solutions and insights into black hole physics, plasma instabilities, and holographic correspondences.

Contribution

It establishes a detailed correspondence between dyonic black holes and magnetohydrodynamics, introduces new stationary solutions, and analyzes plasma instabilities in holographic models.

Findings

Exact agreement of conserved charges between black holes and fluid solutions

Prediction of charged rotating black string properties

Analysis of magnetic field effects on plasma instabilities

Abstract

We use the AdS/CFT correspondence to argue that large dyonic black holes in anti-de Sitter spacetime are dual to stationary solutions of the equations of relativistic magnetohydrodynamics on the conformal boundary of AdS. The dyonic Kerr-Newman-AdS_4 solution corresponds to a charged diamagnetic fluid not subject to any net Lorentz force, due to orthogonal magnetic and electric fields compensating each other. The conserved charges, stress tensor and R-current of the fluid are shown to be in exact agreement with the corresponding quantities of the black hole. Furthermore, we obtain stationary solutions of the Navier-Stokes equations in four dimensions, which yield predictions for (yet to be constructed) charged rotating black strings in AdS_5 carrying nonvanishing momentum along the string. Finally, we consider Scherk-Schwarz reduced AdS gravity on a circle. In this theory, large black holes and black strings are dual to lumps of deconfined plasma of the associated CFT. We analyze the effects that a magnetic field introduces in the Rayleigh-Plateau instability of a plasma tube, which is holographically dual to the Gregory-Laflamme instability of a magnetically charged black string.