Built on

B. Carter, “Hamilton-Jacobi and Schrödinger separable solutions of Einstein’s equations,” Commun. Math. Phys. 10
1968
Earlier work this paper cites.
J. F. Plebański, “A class of solutions of Einstein-Maxwell equations,” Annals Phys. 90
1975
Earlier work this paper cites.
J. F. Plebański and M. Demiański, “Rotating, charged, and uniformly accelerating mass in general relativity,” Annals Phys. 98
1976
Earlier work this paper cites.
J. D. Bjorken, “Highly relativistic nucleus-nucleus collisions: The central rapidity region,” Phys. Rev. D 27
1983
Earlier work this paper cites.
V. Balasubramanian and P. Kraus, “A stress tensor for anti-de Sitter gravity,” Commun. Math. Phys. 208
1999
Earlier work this paper cites.
D. Klemm, V. Moretti and L. Vanzo, “Rotating topological black holes,” Phys. Rev. D 57
1999
Earlier work this paper cites.
G. Policastro, D. T. Son and A. O. Starinets, “The shear viscosity of strongly coupled N = 4 N=4 supersymmetric Yang-Mills plasma,” Phys. Rev. Lett. 87
2001
Earlier work this paper cites.
N. Andersson and G. L. Comer, “Relativistic fluid dynamics: Physics for many different scales,” Living Rev. Rel. 10
2007
Earlier work this paper cites.
S. Bhattacharyya, V. E. Hubeny, S. Minwalla and M. Rangamani, “Nonlinear fluid dynamics from gravity,” JHEP 0802
Original
2008
Earlier work this paper cites.
M. Van Raamsdonk, “Black hole dynamics from atmospheric science,” JHEP 0805
Original
2008
Earlier work this paper cites.

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Then

D. T. Son and P. Surowka, “Hydrodynamics with triangle anomalies,” Phys. Rev. Lett. 103
Original
2009
Later among the works it cites.
M. M. Caldarelli, O. J. C. Dias, R. Emparan and D. Klemm, “Black holes as lumps of fluid,” JHEP 0904
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Later among the works it cites.
J. Camps, R. Emparan and N. Haddad, “Black brane viscosity and the Gregory-Laflamme instability,” JHEP 1005
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2010
Later among the works it cites.
S. S. Gubser, “Symmetry constraints on generalizations of Bjorken flow,” Phys. Rev. D 82
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S. S. Gubser and A. Yarom, “Conformal hydrodynamics in Minkowski and de Sitter spacetimes,” Nucl. Phys. B 846

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2014

Fluid dynamics on ultrastatic spacetimes and dual black holes

Klemm, Dietmar, Maiorana, Andrea

Understand

We show that the classification of shearless and incompressible stationary fluid flows on ultrastatic manifolds is equivalent to classifying the isometries of the spatial sections.

For a flow on R x S$^2$ this leaves only one possibility, since on the 2-sphere all Killing fields are conjugate to each other, and it is well-known that the gravity dual of such a (conformal) fluid is the spherical KNAdS$_4$ black hole.
On the other hand, in R x H$^2$ the situation is more complicated, since the isometry group of H$^2$ admits elliptic, parabolic and hyperbolic elements.
One might thus ask what the gravity duals of the flows corresponding to these three different cases are.

Built on

B. Carter, “Hamilton-Jacobi and Schrödinger separable solutions of Einstein’s equations,” Commun. Math. Phys. 10
1968
Earlier work this paper cites.
J. F. Plebański, “A class of solutions of Einstein-Maxwell equations,” Annals Phys. 90
1975
Earlier work this paper cites.
J. F. Plebański and M. Demiański, “Rotating, charged, and uniformly accelerating mass in general relativity,” Annals Phys. 98
1976
Earlier work this paper cites.
J. D. Bjorken, “Highly relativistic nucleus-nucleus collisions: The central rapidity region,” Phys. Rev. D 27
1983
Earlier work this paper cites.
V. Balasubramanian and P. Kraus, “A stress tensor for anti-de Sitter gravity,” Commun. Math. Phys. 208
1999
Earlier work this paper cites.
D. Klemm, V. Moretti and L. Vanzo, “Rotating topological black holes,” Phys. Rev. D 57
1999
Earlier work this paper cites.
G. Policastro, D. T. Son and A. O. Starinets, “The shear viscosity of strongly coupled N = 4 N=4 supersymmetric Yang-Mills plasma,” Phys. Rev. Lett. 87
2001
Earlier work this paper cites.
N. Andersson and G. L. Comer, “Relativistic fluid dynamics: Physics for many different scales,” Living Rev. Rel. 10
2007
Earlier work this paper cites.
S. Bhattacharyya, V. E. Hubeny, S. Minwalla and M. Rangamani, “Nonlinear fluid dynamics from gravity,” JHEP 0802
Original
2008
Earlier work this paper cites.
M. Van Raamsdonk, “Black hole dynamics from atmospheric science,” JHEP 0805
Original
2008
Earlier work this paper cites.