Abstract
We find hydrodynamic behavior in large simply spinning five-dimensional Anti-de Sitter black holes. These are dual to spinning quantum fluids through the AdS/CFT correspondence constructed from string theory. Due to the spatial anisotropy introduced by the angular momentum, hydrodynamic transport coefficients are split into groups longitudinal or transverse to the angular momentum, and aligned or anti-aligned with it. Analytic expressions are provided for the two shear viscosities, the longitudinal momentum diffusion coefficient, two speeds of sound, and two sound attenuation coefficients. Known relations between these coefficients are generalized to include dependence on angular momentum. The shear viscosity to entropy density ratio varies between zero and 1/(4π) depending on the direction of the shear. These results can be applied to heavy ion collisions, in which the most vortical fluid was reported recently. In passing, we show that large simply spinning five-dimensional Myers-Perry black holes are perturbatively stable for all angular momenta below extremality.
Highlights
Background metric and thermodynamicsWe investigate the consequences of rotation on the gravity side for the dual field theory
In non-rotating black holes it is known from [55] that the spectrum of quasinormal modes (QNMs) of a global AdS black hole with the horizon topology S3 × R asymptotes to the QNM spectrum in the limit of large black hole radius
1.0 a section on a second hypothesis: We assume that at a = 0, but vanishing angular momentum of the perturbation, j = 0, the Kubo formulae for the two shear viscosities are only mildly modified by the angular momentum anisotropy, and η⊥ is related to the tensor correlator T++T++, while η|| is related to the vector correlator T+3T+3 in analogy to [31]
Summary
Background metric and thermodynamicsWe investigate the consequences of rotation on the gravity side for the dual field theory. Since we have applications to the quark-gluon plasma in mind, we are analyzing the five-dimensional case (5DMPAdS), first studied in [11], and expanded to the higher dimensions in [13, 73]. These black holes live in global AdS5, which means that the spatial coordinates on the AdS-boundary live on a three-sphere, and the topology of the dual field theory is R1 × S3. We discuss the case of large black holes, i.e. black holes with a larger horizon radius, r+ L, compared to the AdS-radius, L This will be referred to as case (i). Case (iii), we consider a large black hole limit on the level of the background metric first and derive fluctuation equations
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