Introduction to Relativistic Hydrodynamics

Relativistic hydrodynamics
What is flow?
Two definitions of flow
1. Flow of energy, W µ = 0 (Landau)
Landau, Lifshitz, Fluid mechanics, Pergamon Press (1959)
u µ
L =
T µ ν uν L
u α L T β α Tβγu γ
L
= 1
ɛ T µ ν uν L
2. Flow of conserved charge, V µ = 0 (Eckart)
Eckart, Phys. Rev. 58, 919 (1940)
u µ
E =
N µ
√
NνN ν
Both definitions are related to each other by Lorentz transformations
November 22nd, 2012 | TUD - IKP | D. Nowakowski | 11
u µ
E = Λµ ν uν µ
µ
W V
L , uµ
L ≈ uµ
E + , uµ
ɛ+Ps E ≈ uµ
L + n
uL μ
u E μ
V μ
W μ