Constraints on Rindler Hydrodynamics

TL;DR

This paper investigates second-order uncharged Rindler hydrodynamics, deriving relations among transport coefficients using entropy current and partition function methods, and verifies these in flat and curved spacetimes.

Contribution

It provides new relations among hydrodynamic transport coefficients at second order for Rindler fluids, unifying entropy current and partition function approaches.

Findings

Derived transport coefficient relations from two methods

Verified relations in flat and curved spacetime examples

Confirmed equivalence of entropy and partition function approaches

Abstract

We study uncharged Rindler hydrodynamics at second order in the derivative expansion. The equation of state of the theory is given by a vanishing equilibrium energy density. We derive relations among the transport coefficients by employing two frameworks. First, by the requirement of having an entropy current with a non-negative divergence, second by studying the thermal partition function on stationary backgrounds. The relations derived by these two methods are equivalent. We verify the results by studying explicit examples in flat and curved space-time geometries.