Flat space compressible fluid as holographic dual of black hole with curved horizon

We consider the fluid dual of $(d+2)$-dimensional vacuum Einstein equation either with or without a cosmological constant. The background solutions admit black hole event horizons and the spatial sections of the horizons are conformally flat. Therefore, a $d$-dimensional flat Euclidean space $\mathbb{E}^d$ is contained in the conformal class of the spatial section of the black hole horizon. A compressible, forced, stationary and viscous fluid system can be constructed on the product (Newtonian) spacetime $\mathbb{R}\times\mathbb{E}^d$ as the lowest order fluctuation modes around such black hole background. This construction provides the first example of holographic duality which is beyond the class of bulk/boundary correspondence.Comment: 14 pages. V3: error corrections. To appear in JHE

The similarity metric

A new class of distances appropriate for measuring similarity relations between sequences, say one type of similarity per distance, is studied. We propose a new ``normalized information distance'', based on the noncomputable notion of Kolmogorov complexity, and show that it is in this class and it minorizes every computable distance in the class (that is, it is universal in that it discovers all computable similarities). We demonstrate that it is a metric and call it the {\em similarity metric}. This theory forms the foundation for a new practical tool. To evidence generality and robustness we give two distinctive applications in widely divergent areas using standard compression programs like gzip and GenCompress. First, we compare whole mitochondrial genomes and infer their evolutionary history. This results in a first completely automatic computed whole mitochondrial phylogeny tree. Secondly, we fully automatically compute the language tree of 52 different languages.Comment: 13 pages, LaTex, 5 figures, Part of this work appeared in Proc. 14th ACM-SIAM Symp. Discrete Algorithms, 2003. This is the final, corrected, version to appear in IEEE Trans Inform. T

Fluids and vortex from constrained fluctuations around C-metric black hole

By foliating the four-dimensional C-metric black hole spacetime, we consider a kind of initial-value-like formulation of the vacuum Einstein's equation, the holographic initial data is a double consisting of the induced metric and the Brown-York energy momentum tensor on an arbitrary initial hypersurface. Then by perturbing the initial data that generates the background spacetime, it is shown that, in an appropriate limit, the fluctuation modes are governed by the continuity equation and the compressible Navier-Stokes equation which describe the momentum transport in non-relativistic viscous fluid on a flat Newtonian space. It turns out that the flat space fluid behaves as a pure vortex and the viscosity to entropy ratio is subjected to the black hole acceleration.Comment: 19 pages, LaTeX. v2: added a new reference. v3: major revisio