Introduction to Relativistic Hydrodynamics

Relativistic viscous hydrodynamics
Basic equations
◮ allow dissipative terms, but no charge in the system
◮ assume entropy current has additional linear dissipative terms (first-order
theory)
S µ = su µ + αV µ
◮ phenomenological definitions resp. so called constitutive equations for the
shear stress tensor π µν and for the bulk pressure Π
π µν
1
= 2η ∆
2
µ α∆ ν β + ∆µ
β∆ν
α − 1
3 ∆µν
∆αβ ∆ ακ ∂κu β
Π = −ξ∂µu µ
◮ transport coefficients: η shear viscosity, ξ bulk viscosity, ...
◮ characterize deviation from thermal equilibrium
November 22nd, 2012 | TUD - IKP | D. Nowakowski | 17