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Register a new userFluid Super-Dynamics from Black Hole Superpartners
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Recently the Navier-Stokes equations have been derived from the duality with the black branes in AdS_5. The zero modes of black branes are reinterpreted as dynamical degrees of freedom of a conformal fluid on the boundary of AdS_5. Here, we derive the corrections to the Navier-Stokes equations due to fermionic zero modes of the black branes. We study only the contributions due to bilinears in the fermionic zero modes in the first order of the parameter expansion. The need of a superextension of the fluid dynamics is a consequence of the full AdS/CFT correspondence and yet to be investigated.
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We reconstruct the complete fermionic orbit of the non-extremal BTZ black hole by acting with finite supersymmetry transformations. The solution satisfies the exact supergravity equations of motion to all orders in the fermonic expansion and the final result is given in terms of fermionic bilinears. By fluid/gravity correspondence, we derive linearized Navier-Stokes equations and a set of new differential equations from Rarita-Schwinger equation. We compute the boundary energy-momentum tensor and we interpret the result as a perfect fluid with a modified definition of fluid velocity. Finally, we derive the modified expression for the entropy of the black hole in terms of the fermionic bilinears.
We generalise the computations of arXiv:0712.2456 to generate long wavelength, asymptotically locally AdS_5 solutions to the Einstein-dilaton system with a slowly varying boundary dilaton field and a weakly curved boundary metric. Upon demanding regularity, our solutions are dual, under the AdS/CFT correspondence, to arbitrary fluid flows in the boundary theory formulated on a weakly curved manifold with a prescribed slowly varying coupling constant. These solutions turn out to be parametrised by four-velocity and temperature fields that are constrained to obey the boundary covariant Navier Stokes equations with a dilaton dependent forcing term. We explicitly evaluate the stress tensor and Lagrangian as a function of the velocity, temperature, coupling constant and curvature fields, to second order in the derivative expansion and demonstrate the Weyl covariance of these expressions. We also construct the event horizon of the dual solutions to second order in the derivative expansion, and use the area form on this event horizon to construct an entropy current for the dual fluid. As a check of our constructions we expand the exactly known solutions for rotating black holes in global AdS_5 in a boundary derivative expansion and find perfect agreement with all our results upto second order. We also find other simple solutions of the forced fluid mechanics equations and discuss their bulk interpretation. Our results may aid in determining a bulk dual to forced flows exhibiting steady state turbulence.
Black branes in AdS5 appear in a four parameter family labeled by their velocity and temperature. Promoting these parameters to Goldstone modes or collective coordinate fields -- arbitrary functions of the coordinates on the boundary of AdS5 -- we use Einsteins equations together with regularity requirements and boundary conditions to determine their dynamics. The resultant equations turn out to be those of boundary fluid dynamics, with specific values for fluid parameters. Our analysis is perturbative in the boundary derivative expansion but is valid for arbitrary amplitudes. Our work may be regarded as a derivation of the nonlinear equations of boundary fluid dynamics from gravity. As a concrete application we find an explicit expression for the expansion of this fluid stress tensor including terms up to second order in the derivative expansion.
We examine the real-time dynamics of a system of one or more black holes interacting with long wavelength gravitational fields. We find that the (classical) renormalizability of the effective field theory that describes this system necessitates the introduction of a time dependent mass counterterm, and consequently the mass parameter must be promoted to a dynamical degree of freedom. To track the time evolution of this dynamical mass, we compute the expectation value of the energy-momentum tensor within the in-in formalism, and fix the time dependence by imposing energy-momentum conservation. Mass renormalization induces logarithmic ultraviolet divergences at quadratic order in the gravitational coupling, leading to a new time-dependent renormalization group (RG) equation for the mass parameter. We solve this RG equation and use the result to predict heretofore unknown high order logarithms in the energy distribution of gravitational radiation emitted from the system.
We present a new family of asymptotic AdS_3 x S^2 solutions to eleven dimensional supergravity compactified on a Calabi-Yau threefold. They originate from the backreaction of S^2-wrapped M2-branes, which play a central role in the deconstruction proposal for the microscopic interpretation of the D4-D0 black hole entropy. We show that they are free of possible pathologies such as closed timelike curves and discuss their holographic interpretation.
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