Magnetohydrodynamics from gravity

Abstract

Imposing the Petrov-like boundary condition on the hypersurface at finite cutoff, we derive the hydrodynamic equation on the hypersurface from the bulk Einstein equation with electromagnetic field in the near horizon limit. We first get the general framework for spacetime with matter field, and then derive the incompressible Navier-Stokes equations for black holes with electric charge and magnetic charge respectively. Especially, in the magnetic case, the standard magnetohydrodynamic equations will arise due to the existence of the background electromagnetic field on the hypersurface.Comment: 21 page

Fluid/gravity duality with Petrov-like boundary condition in a spacetime with a cosmological constant

“…Secondly, when a matter field is taken into account, besides extending the framework to including the contribution from the matter field in the Petrov-like boundary condition, it also involves how to put appropriate boundary conditions on the cutoff surface for the matter field itself when it is also dynamical and has some degrees of freedom. We will construct a model with Maxwell field and provide an affirmative answer to this issue elsewhere [29]. Therefore, based on all investigations mentioned above we may conjecture that at least in the near horizon limit, imposing Petrov-like condition on the boundary should be a universal method to reduce the Einstein equation to the Navier-Stokes equation for a general spacetime in the presence of a horizon.…”

Holographic parity-violating charged fluid dual to Chern-Simons modified gravity

“…(21) and (23) with solutions (18). With these incompressible and nonvortical conditions, a new constraint condition at Oðϵ 3 Þ reads as…”

“…We can also try to set up the holographic duality between the nondynamical CS gravity and ð2 þ 1Þ-dimensional vortical fluid in the cutoff flat surface Σ c , namely, Ω ≠ 0. Notice that the expressions for C (18)]. As in Ref.…”

“…Imposing the Petrov-like condition on the Σ c ðr ¼ r c Þ in the near horizon limit, the incompressible Navier-Stokes equations (or modified equations) for a fluid living on the flat (or spatially curved) spacetime with one fewer dimensions have been demonstrated in Refs. [15][16][17][18][19][20][21]. The physics on a finite cutoff surface Σ c with finite energy scale is appealing since it could be reached by experiments.…”

Tópicos da correspondência fluido gravidade em espaços planos

“…Further developments of this fluid/gravity correspondence include a procedure similar to the one developed in [25], that applies the reasoning of ε-expansion in the relativistic case [26][27][28], the discussion of Petrov types [29], the possibility of a similar correspondence for magnetohydrodynamics [30,31], as well as the AdS/Ricci-flat correspondence [32,33], which relates a class of asymptotically anti-de Sitter spacetimes with another class of Ricci-flat spacetimes and therefore may provide a bridge between the AdS cases and the Rindler ones.…”