Black hole-black string phase transitions from hydrodynamics

TL;DR

The paper uses the fluid/gravity correspondence to study phase transitions of deconfined plasma lumps in Scherk-Schwarz compactified AdS backgrounds, identifying plasma ball, uniform tube, and non-uniform tube as fluid duals to localized black holes and strings with horizons $S^{d}$ or $S^{d-1}\times S^1$. By solving relativistic Navier-Stokes equations with a surface term and adopting a Scherk-Schwarz equation of state, it derives constant mean curvature equilibria and constructs microcanonical and canonical phase diagrams across dimensionally varied regimes. The results reveal critical dimensions where smooth UT$\rightarrow$NUT transitions become possible and show qualitative agreement with the behavior of black hole–black string systems in Kaluza-Klein spacetimes, including RP/GL-type instabilities and their holographic interpretation. The findings suggest a deeper universality in high-dimensional gravitational phase structure and point to future work in obtaining explicit gravity duals and extending to rotating/plasma-ring configurations.

Abstract

We discuss the phase transitions between three states of a plasma fluid (plasma ball, uniform plasma tube, and non-uniform plasma tube), which are dual to the corresponding finite energy black objects (black hole, uniform black string, and non-uniform black string) localized in an asymptotically locally AdS space. Adopting the equation of state for the fluid obtained by the Scherk-Schwarz compactification of a conformal field theory, we obtain axisymmetric static equilibrium states of the plasma fluid and draw the phase diagrams with their thermodynamical quantities. By use of the fluid/gravity correspondence, we predict the phase diagrams of the AdS black holes and strings on the gravity side. The thermodynamic phase diagrams of the AdS black holes and strings show many similarities to those of the black hole-black string system in a Kaluza-Klein vacuum. For instance, the critical dimension for the smooth transition from the uniform to non-uniform strings is the same as that in the Kaluza-Klein vacuum in the canonical ensemble. The analysis in this paper may provide a holographic understanding of the relation between the Rayleigh-Plateau and Gregory-Laflamme instabilities via the fluid/gravity correspondence.

Figures (6)

• Figure 1: An axisymmetric static equilibrium state of fluid in a $d=(n+3)$-dimensional flat spacetime schematically embedded in a three dimensional space.
• Figure 2: (a) The non-uniform tube in $d=4$ is called Delaunay's unduloid in geometry, which is the surface of revolution of an elliptic catenary. The elliptic catenary is obtained by rotating an ellipse along a line (i.e., the $z$-axis) and tracing the focus, marked by small solid circles. (b) A schematic picture of the potential $U(w)$, defined in Eq. (\ref{['eq:potential-form']}), for three values of $\lambda=w_-/w_+$. From the top curve to the bottom, the value of $\lambda$ decreases within the range $0<\lambda<1$.
• Figure 3: The energy-entropy diagram for $d=5$, containing the phases of the spherical ball (SB, blue-solid line), uniform tube (UT, black-dashed curve), and non-uniform tube (NUT, red-solid curve with small circles of data). The maximum entropy state for a given energy is favored. There is no cusp on the non-uniform tube phase, which is the case for $4 \leq d \leq 9$.
• Figure 4: The energy-entropy diagrams for (a) $d=10$, (b) $d=11$, and (c) $d=12$. There appear two cusps on the non-uniform tube phase in this class of dimensions.
• Figure 5: The energy-entropy diagram for $d=13$. There exists one cusp on the non-uniform tube phase, which is the case for $d \geq 13$.