Abstract
We study the surface transport properties of stationary localized configurations of relativistic fluids to the first two non-trivial orders in a derivative expansion. By demanding that these finite lumps of relativistic fluid are described by a thermal partition function with arbitrary stationary background metric and gauge fields, we are able to find several constraints among surface transport coefficients. At leading order, besides recovering the surface thermodynamics, we obtain a generalization of the Young-Laplace equation for relativistic fluid surfaces, by considering a temperature dependence in the surface tension, which is further generalized in the context of superfluids. At the next order, for uncharged fluids in 3+1 dimensions, we show that besides the 3 independent bulk transport coefficients previously known, a generic localized configuration is characterized by 3 additional surface transport coefficients, one of which may be identified with the surface modulus of rigidity. Finally, as an application, we study the effect of temperature dependence of surface tension on some explicit examples of localized fluid configurations, which are dual to certain non-trivial black hole solutions via the AdS/CFT correspondence.
Highlights
Them with a few effective degrees of freedom — the fluid fields
Besides recovering the surface thermodynamics, we obtain a generalization of the Young-Laplace equation for relativistic fluid surfaces, by considering a temperature dependence in the surface tension, which is further generalized in the context of superfluids
For uncharged fluids in 3+1 dimensions, we show that besides the 3 independent bulk transport coefficients previously known, a generic localized configuration is characterized by 3 additional surface transport coefficients, one of which may be identified with the surface modulus of rigidity
Summary
Consider a relativistic fluid living in a spacetime N , equipped with a time-like Killing vector, which has the most general stationary metric. Gij is the metric on spatial manifold obtained by reducing on the time-circle, which we shall denote by Ns. In some of our discussions, we will include a conserved global U(1). We shall denote the fluid surface by f (x) = 0, where f (x) is taken to be independent of time, following our stationary assumption. The second term in (1.9) is the main focus of this paper, and in particular cases, we shall provide the explicit forms of the surface partition function, up to the first non-trivial orders in derivatives. This equation of motion for f (x) is identical to the particular surface fluid equation which follows by demanding diffeomorphism invariance in directions orthogonal to the surface.
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