Black Holes as Lumps of Fluid

Abstract

The old suggestive observation that black holes often resemble lumps of fluid has recently been taken beyond the level of an analogy to a precise duality. We investigate aspects of this duality, and in particular clarify the relation between area minimization of the fluid vs. area maximization of the black hole horizon, and the connection between surface tension and curvature of the fluid, and surface gravity of the black hole. We also argue that the Rayleigh-Plateau instability in a fluid tube is the holographic dual of the Gregory-Laflamme instability of a black string. Associated with this fluid instability there is a rich variety of phases of fluid solutions that we study in detail, including in particular the effects of rotation. We compare them against the known results for asymptotically flat black holes finding remarkable agreement. Furthermore, we use our fluid results to discuss the unknown features of the gravitational system. Finally, we make some observations that suggest that asymptotically flat black holes may admit a fluid description in the limit of large number of dimensions.

Figures (6)

• Figure 1: Entropy versus energy phase diagrams. The entropy is normalized to be one for uniform plasma tubes. Uniform plasma tubes, plasma balls and non-uniform plasma tubes correspond to squares, circles and triangles respectively. The left diagram, plotted for $n=1$, is representative for $n\leq7$, and shows that the preferred configuration is the plasma ball for small energy, and the uniform plasma tube for higher energy. The unstable plasma ball branch merges with the non-uniform plasma tube branch in the merger point. Above the critical dimension, for $n\geq8$ (the right diagram corresponds to $n=12$), the non-uniform plasma tubes become stable and become the preferred configuration for an intermediate range of energies. The left figure should be compared with Fig. 3 of Harmark:2005pp for the phases of non-uniform black strings. To plot these diagrams we used the values $\alpha=1$, $\rho_0=0$ and $\sigma=1$.
• Figure 2: Figures of equilibrium of a rotating plasma tube. From left to right, an ordinary non-uniform rotating plasma tube ($v_m=.5$, $v_o=.8$, $k=.628024$), a pinched plasma tube ($v_m=.201016$, $v_o=.918$, $k=.15$) and a plasma tube on the verge of splitting off a plasma ring ($v_m=.201016$, $v_o=.9133$, $k=.15$). The parameters have been chosen such that the three tubes share the same periodicity.
• Figure 3: Figures of equilibrium of a rotating plasma ball. From left to right, an ordinary rotating drop ($v_o=.7$, $k=2$), a marginal rotating drop ($v_o=.1$, $k=21$), a pinched plasma ball ($v_o=.5$, $k=.83$) and a pinched ball on the verge of splitting of a plasma ring ($v_o=.7965$, $k=.5$).
• Figure 4: Figures of equilibrium of a rotating plasma ring. On the left, a thin plasma ring ($v_{\rm i}=.2$, $v_o=.6$, $k=9$) and on the right a fat plasma ring ($v_{\rm i}=.1$, $v_o=.4$, $k=2$).
• Figure 5: Plot of the dimensionless dispersion relation $\omega(k)$ for the Rayleigh-Plateau instability in a static uniform tube for several spacetime dimensions $d=n+3$. The instability strength and threshold wavenumber increase as the spacetime dimension grows. Intuitively, this is because the "same" perturbation decreases more the surface area of the plasma boundary (increases more the plasma entropy) as the dimension increases. Note also that the most unstable mode satisfies $\omega R_o{\bigl |}_{\rm max} \gg \frac{\sigma}{\rho_0 R_o}$, and is thus within the regime of validity of the hydrodynamic description (see section \ref{['sec:RegimeValidity']}). This plot is to be qualitatively compared with Fig. 3 of Gregory:1994bj for the GL instability.