Abstract
The fluid/gravity correspondence establishes how gravitational dynamics, as dictated by Einstein's field equations, are related to the fluid dynamics, governed by the relativistic Navier–Stokes equations. In this work the correspondence is extended, where the duality between incompressible fluids and gravitational backgrounds with soft hair excitations is implemented. This construction is set through appropriate boundary conditions to the gravitational background, leading to a correspondence between generalized incompressible Navier–Stokes equations and soft hairy horizons.
Highlights
AdS/CFT is well known to assert the duality between N = 4 SU(N ) super Yang-Mills theory and type IIB string theory with AdS5 × S5 compactification [1]
Besides the influential developments in Refs. [22,23,24,25], with these new boundary conditions we study a possible generalization of the incompressible Navier–Stokes equations describing the dual fluid at a soft hairy horizon
In this work we have shown how to generalize the particular realization of the fluid/gravity correspondence in Ref. [19] by considering a new set of horizon boundary conditions, which are associated with soft hair excitations
Summary
In the long wavelength regime, the conservation of the energy-momentum tensor is led to hydrodynamics, as an explicit correspondence between gravity and fluid dynamics It consists of the fluid/gravity correspondence, where solutions of relativistic hydrodynamics on the boundary yield solutions of Einstein’s field equations, describing black holes [2,3,4]. [22,23,24,25], with these new boundary conditions we study a possible generalization of the incompressible Navier–Stokes equations describing the dual fluid at a soft hairy horizon.
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