Second order causal hydrodynamics in Eckart frame: using gradient expansion scheme

TL;DR

This paper develops a second-order causal relativistic hydrodynamics framework in the Eckart frame using gradient expansion, with applications to astrophysical phenomena like accretion disks and neutron stars.

Contribution

It introduces a second-order causal hydrodynamics formalism in the Eckart frame incorporating curvature effects, extending previous models.

Findings

Formalism includes curvature terms in flux quantities

Applicable to astrophysical systems with strong gravity

Provides a basis for modeling viscous accretion disks and neutron stars

Abstract

In the present work, we develop a causal theory of relativistic non-ideal fluids up to the second order in the Eckart frame using gradient expansion scheme. Keeping the spirit of Mueller-Israel-Stewart formalism, the general forms of bulk viscosity, shear viscosity tensor and the heat flow vector are presented. Since each of the flux quantities explicitly carry curvature terms, we show that our formalism finds application in astrophysics in particular in the strong gravity regime. We elucidate two such applications namely in viscous thick accretion disks also known as Polish doughnuts and in addressing non-rotating equilibrium configuration, like neutron stars.