Initial Data for First-order Causal Viscous Conformal Fluids in General Relativity

TL;DR

This paper develops initial data solutions for a first-order causal viscous conformal fluid in general relativity, combining conformal methods with perturbation techniques to address the complexities of the Einstein constraint equations.

Contribution

It introduces a novel approach to solving Einstein constraint equations for viscous conformal fluids by integrating conformal methods with perturbative analysis.

Findings

Successfully constructed initial data for viscous conformal fluids in GR.

Demonstrated that direct conformal methods do not decouple equations for this theory.

Provided a perturbative framework to overcome the coupling challenges.

Abstract

We solve the Einstein constraint equations for a first-order causal viscous relativistic hydrodynamic theory in the case of a conformal fluid. For such a theory, a direct application of the conformal method does not lead to a decoupling of the equations, even for constant-mean curvature initial data. We combine the conformal method applied to a background perfect fluid theory with a perturbative argument in order to obtain the result.