Dyonic AdS black holes from magnetohydrodynamics

TL;DR

The paper establishes a holographic bridge between dyonic AdS black holes and stationary magnetohydrodynamics on the conformal boundary, showing that large KN–AdS$_4$ black holes are dual to diamagnetic boundary fluids with conserved charges and stress tensors precisely matching the gravity data. By deriving MHD from gravity and solving the Navier–Stokes equations in various geometries, the authors predict duals for rotating charged black strings in AdS$_5$ and extend the framework to Scherk–Schwarz AdS gravity, where magnetic fields influence plasma tube instabilities. They compute the grand-canonical function $h(\nu,b)$ from static black holes, reproduce KN-AdS$_4$ thermodynamics via boundary data, and demonstrate that magnetic fields weaken the Rayleigh–Plateau instability, with implications for Gregory–Laflamme-type transitions in magnetized AdS strings. The work provides a comprehensive hydrodynamic toolkit to explore new gravitational solutions, stability, and phase structure in holographic contexts with external magnetic fields, connecting fluid dynamics, CFT plasmas, and AdS black objects in a unified framework.

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.

Figures (1)

• Figure 1: Plot of the dimensionless dispersion relation $\omega(k)$ for the Rayleigh-Plateau instability in a static uniform tube for several values of the axial magnetic field ${\cal B}_{(0)}$ (in the plot, $B$). The instability strength and decreases as the magnetic field grows. We use (\ref{['Pert:Dispersion']}) and the numerical data correspond to take $\frac{\sigma}{(\rho_{(0)}+{\cal P}_{(0)})R_0}=\frac{10^{-6}}{5-2{\cal B}_{(0)}^2}$ (see text).