Two theorems for the gradient expansion of relativistic hydrodynamics

Abstract

This letter is dedicated to providing proof of two statements concerning the gradient expansion of relativistic hydrodynamics. The first statement is that \textit{the ordering of transverse derivatives is irrelevant in the gradient expansion of a non-conformal fluid}. The second statement is that \textit{the longitudinal projection of the Weyl covariant derivative can be eliminated in the gradient expansion of a conformal fluid}. This second statement does not apply to curvature tensors. In the conformal case, we know that the ordering of Weyl covariant derivatives is irrelevant in the gradient expansion.

6 pages; Published in Physics Letters B

References in corpus (8)

• Nonlinear Fluid Dynamics from Gravity
• Gravity & Hydrodynamics: Lectures on the fluid-gravity correspondence
• Entropy Current in Conformal Hydrodynamics
• On the convergence of the gradient expansion in hydrodynamics
• The Fluid/Gravity Correspondence: a new perspective on the Membrane Paradigm
• Transient Relativistic Fluid Dynamics in a General Hydrodynamic Frame
• Hydrodynamic gradient expansion in linear response theory
• All Order Linearized Hydrodynamics from Fluid/Gravity Correspondence