Thermodynamics of Plasmaballs and Plasmarings in 3+1 Dimensions

TL;DR

This work uses the AdS/CFT correspondence to study rotating, localized plasma configurations in 3+1 dimensions arising from Scherk-Schwarz compactification, predicting the thermodynamics of localized black holes and black rings in Scherk-Schwarz AdS_6. It derives an exact relativistic Navier–Stokes solution in the thin-ring limit, complemented by a thorough numerical analysis that maps the full thermodynamic phase space. The study confirms ball and ring (including pinched-ball) as the stationary rotating fluid solutions and reveals a continuous ball→pinched-ball→thin-ring transition, with the thin ring dominating the entropy at large angular momentum, and contrasts these results with conjectured flat-space phase diagrams. The results illuminate how AdS curvature and SS compactification qualitatively alter horizon topology phases and offer a controlled framework for investigating stability and dynamics of higher-dimensional black holes and rings via boundary fluid dynamics.

Abstract

We study localized plasma configurations in 3+1 dimensional massive field theories obtained by Scherk-Schwarz compactification of 4+1 dimensional CFT to predict the thermodynamic properties of localized blackholes and blackrings in Scherk-Schwarz compactified $AdS_6$ using the AdS/CFT correspondence. We present an exact solution to the relativistic Navier-Stokes equation in the thin ring limit of the fluid configuration. We also perform a thorough numerical analysis to obtain the thermodynamic properties of the most general solution. Finally we compare our results with the recent proposal for the phase diagram of blackholes in six flat dimensions and find some similarities but other differences.

Figures (9)

• Figure 1: Schematic plot of the phase diagram for the various plasma configurations which by AdS/CFT correspondence gives the phase structure of blackholes with various horizon topologies in Scherk-Schwarz compactified $AdS_6$.
• Figure 2: Here we plot entropy ($\tilde{S}$) against angular momentum ($\tilde{L}$) for $\tilde{E}=10$ (note that even when the thin ring approximation is invalid for such low energies this plot agrees quite well with the numerical plots presented in §5.
• Figure 3: Here we again plot entropy ($\tilde{S}$) against angular momentum ($\tilde{L}$) for different fixed energies ($\tilde{E} = 3000, 5000, 6000, 7000$) within the domain of validity of the thin ring approximation. for all the plots the left end is the point where $\alpha$ is 0.1 and the right end is the point where the hydrodynamics assumption starts breaking down.
• Figure 4: In $(a)$ we plot $\tilde{h}(v)$ (the plot at the side shows $\tilde{h}(v)$ near $v=v_i$) and in $(b)$ we plot $\tilde{h}^\prime(v)$. All the plots are for $v_o=0.74$ and the value of $v_i$ are $0.01, 0.001, 0, 0001, 10^{-14}$ as we go from top to bottom.
• Figure 5: Allowed region of energy (x-axis) and angular momentum (y-axis) space for ordinary ball solution.