The Relativistic Rindler Hydrodynamics

TL;DR

This paper explores the holographic duality between certain (d+2)-dimensional geometries and relativistic fluids in (d+1) dimensions, deriving second-order hydrodynamics and analyzing the physical properties of these solutions.

Contribution

It introduces a new class of holographic geometries dual to relativistic fluids and constructs the corresponding second-order hydrodynamics with entropy current analysis.

Findings

Identified Rindler and Taub geometries as solutions to Einstein equations.

Constructed second-order relativistic hydrodynamics for the Rindler fluid.

Confirmed positivity of the entropy current divergence.

Abstract

We consider a (d+2)-dimensional class of Lorentzian geometries holographically dual to a relativistic fluid flow in (d+1) dimensions. The fluid is defined on a (d+1)-dimensional time-like surface which is embedded in the (d+2)-dimensional bulk space-time and equipped with a flat intrinsic metric. We find two types of geometries that are solutions to the vacuum Einstein equations: the Rindler metric and the Taub plane symmetric vacuum. These correspond to dual perfect fluids with vanishing and negative energy densities respectively. While the Rindler geometry is characterized by a causal horizon, the Taub geometry has a timelike naked singularity, indicating pathological behavior. We construct the Rindler hydrodynamics up to the second order in derivatives of the fluid variables and show the positivity of its entropy current divergence.