Introduction to Relativistic Hydrodynamics

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Relativistic hydrodynamics Parametrization of hydrodynamical quantities ◮ energy-momentum tensor T µν (10 independent components) T µν = ɛu µ u ν − P∆ µν + W µ u ν + W ν u µ + π µν u µ , ∆ µν = g µν − u µ u ν “projection vector, tensor” ɛ energy density P = PS + Π hydrostatic + bulk pressure W µ energy / heat current π µν shear stress tensor ◮ conserved current N µ i (4 · k independent components) ni = uµN µ i V µ i = ∆µ ν N ν i November 22nd, 2012 | TUD - IKP | D. Nowakowski | 9 N µ i = niu µ + V µ i charge density charge current g µν = diag(1, −13×3)
Relativistic hydrodynamics Basic equations ◮ projection vector and tensor are orthogonal to each other ◮ each term of T µν and N µ i uµ∆ µν = 0 can be obtained by contraction of these quantities with u µ and ∆ µν or combinations of them, like P = − 1 3 ɛ = uµT µν uν ∆µνT µν ◮ need initial / boundary conditions and equation of state November 22nd, 2012 | TUD - IKP | D. Nowakowski | 10
Page 1 and 2: Introduction to Relativistic Hydrod
Page 3 and 4: Heavy ion collisions A very naive p
Page 5 and 6: Relativistic hydrodynamics Introduc
Page 7: Relativistic hydrodynamics Basic eq
Page 11 and 12: Relativistic hydrodynamics Overview
Page 13 and 14: Relativistic ideal hydrodynamics Lo
Page 15 and 16: Relativistic viscous hydrodynamics
Page 17 and 18: Relativistic viscous hydrodynamics
Page 19 and 20: Relativistic hydrodynamics Equation
Page 21 and 22: Heavy ion collisions November 22nd,
Page 23 and 24: Heavy ion collisions Schematic time
Page 25 and 26: Heavy ion collisions Initial condit
Page 27 and 28: Heavy ion collisions Bjorken model
Page 33 and 34: Heavy ion collisions Bjorken model:
Page 35 and 36: Heavy ion collisions Bjorken model:
Page 37 and 38: Heavy ion collision and the Bjorken
Page 39 and 40: Outlook “... it is by no means cl

Introduction to Relativistic Hydrodynamics

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