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

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.

20 pages, a new section added, accepted for publication in Classical and Quantum Gravity, matches with published version

References in corpus (5)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Kubo Formulae for Second-Order Hydrodynamic Coefficients
• Landau and Eckart frames for relativistic fluids in nuclear collisions

Cited by in corpus (6)

• Stationary models of magnetized viscous tori around a Schwarzschild black hole
• Phenomenological Relativistic Second-Order Hydrodynamics for Multiflavor Fluids
• Dynamical spectral structure of density fluctuation near QCD critical point
• Gravito-thermal transports, Onsager reciprocal relation and gravitational Wiedemann-Franz law
• Two theorems for the gradient expansion of relativistic hydrodynamics
• Holographic Constraints on Generalised Rivlin-Ericksen Fluid