Abstract
We realize the weak momentum relaxation in Rindler fluid, which lives on the time-like cutoff surface in an accelerating frame of flat spacetime. The translational invariance is broken by massless scalar fields with weak strength. Both of the Ward identity and the momentum relaxation rate of Rindler fluid are obtained, with higher order correction in terms of the strength of momentum relaxation. The Rindler fluid with momentum relaxation could also be approached through the near horizon limit of cutoff AdS fluid with momentum relaxation, which lives on a finite time-like cutoff surface in Anti-de Sitter(AdS) spacetime, and further could be connected with the holographic conformal fluid living on AdS boundary at infinity. Thus, in the holographic Wilson renormalization group flow of the fluid/gravity correspondence with momentum relaxation, the Rindler fluid can be considered as the Infrared Radiation(IR) fixed point, and the holographic conformal fluid plays the role of the ultraviolet(UV) fixed point.
Highlights
With a Dirichlet cutoff surface outside the horizon, the causal structure of the Rindler spacetime with a cutoff is similar to the Poincare patch of AdS spacetime, which provides one frame to study the holography in flat spacetime and motivate us to study the Rindler fluid in more details
The translational invariance is broken by massless scalar fields with weak strength
The Rindler fluid with momentum relaxation could be approached through the near horizon limit of cutoff AdS fluid with momentum relaxation, which lives on a finite time-like cutoff surface in Anti-de Sitter(AdS) spacetime, and further could be connected with the holographic conformal fluid living on AdS boundary at infinity
Summary
If we consider k as a small parameter, the following p + 2 dimensional Rindler metric with corrections of order k2, is a perturbed solution of the field equations (2.2) up to k2, ds2p+2 = −2κ0 (r − r0 )dt2 + 2dtdr + δijdxidxj p (r r0 )(r rc )k2dt. In order to study the fluid dual to Rindler spacetime with momentum relaxation, we make the following coordinate transformation λ2. As the usual set up in Rindler fluid, we need to make the boost transformation associated with the hypersurface dt → −uadxa, δijdxidxj → habdxadxb, with the projection tensor hab = ηab + uaub We assume both of the (p + 1) velocity ua and the position of the horizon r0 in (2.8) to be xa dependent. We will confirm these results from the near horizon limit of the cutoff AdS fluid
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