Perfect Fluids

In General > s.a. gas.
* Idea: A fluid with isotropic pressure, no viscosity and (in general relativity) no heat conduction; It is described by a four-velocity u^a, number density , energy density , pressure p, specific entropy s, temperature T, relativistic enthalpy h; Of the scalar quantities, only two are independent, to define the rest use the equation of state and the first law of thermodynamics; If = (, s), then

h = / = ( + p)/ ,      T = ( / s) / ,       and       p = h – .

* Stress-energy tensor: Of the form

T_ab = ( + p) u_a u_b + p g_ab ,

derivable from the Lagrangian L = – , where the variations are subject to constraints; The field equations are stress-energy conservation, _a T^ab = 0, together with either the continuity equation _a( u^a) = 0, or u^a _a s = 0.
* 3+1 Equations: The conservation of stress-energy, _a T^ab = 0, gives, projected parallel and perpendicular to u^a, respectively,

_a( u^a) = – p _a u^a       and       ( + p) u^a _a v^b = – q^ab _a p

(conservation of mass-energy and momentum, respectively); The Newtonian limit of the second equation is the Euler equation.

Types, Couplings and Applications > s.a. Chaplygin Gas; Phantom Field; relativistic cosmological models and matter.
* Isentropic: One with an equation of state of the form p = p() only; In this case, one can introduce the elastic potential (or internal energy) and the density , with = (1 + ).
@ Null dust: Kijowski et al PRD(90); Bicák & Kuchar PRD(97)gq [canonical general relativity].
@ Other types: Quevedo & Sussman CQG(95)gq/94 [non-isentropic, thermodynamics]; Jackiw et al JPA(04)hp [with internal symmetry and susy].
> In general relativity: see canonical general relativity with matter; relativistic cosmology and cosmological models, in particular FRW spacetimes; 3-dimensional and numerical relativity; solutions, solutions with symmetries, spherically symmetric, and generation methods.

References
@ General: Thorne in(67); Misner in(68); in Hawking & Ellis 73, 69ff; in Misner et al 73; Smarr et al in(80); Anile 89.
@ Variational formulation: Schutz & Sorkin AP(77); Kopczynski AP(90); Dimitrov gq/99, gq/99; Elze et al JPG(99)hp; Marsden et al JGP(01) [general continuum mechanics].
@ Lagrangian, Hamiltonian: Bao et al CMP(85); Bombelli & Torrence CQG(90); Brown CQG(93), AP(96)gq/94; Langlois in(94); Peitz & Appl gq/97/MNRAS [3+1]; Morrison RMP(98); Antoniou & Pronko TMP(04)ht/01 [and Clebsch variables]; Manoff gq/02-in, gq/03 [Lagrangian]; Bhat mp/04 [compressible]; Kolev a0711 [Poisson brackets].
@ Covariant: Bruni & Sopuerta CQG(03)gq [long-wavelength].
@ Numerical implementation: Papadopoulos & Font PRD(00)gq/99 [spherical]; Baumgarte et al gq/99-in [3D].
@ Relativistic: Schutz PRD(71) [Hamiltonian]; Calzetta CQG(98)gq/97 [fluctuating]; Walton ap/05 [symmetric hyperbolic Euler equations]; Gourgoulhon gq/06-ln; Borshch & Zhdanov a0709-in [exact non-stationary non-homogeneous flows].
@ Quantization: Roberts MPAG(98)gq.
@ Related topics: Zloshchastiev APPB(99)gq/98 [models for Lorentzian geometry]; Ghosh ht/01 [as gauge theory], ht/01 [conserved quantities]; Verozub gq/07/IJMPD [particles as moving along geodesics].

Main page – Abbreviations – Journals – Comments – Other sites – Acknowledgements
Send feedback and suggestions to bombelli at olemiss.edu – Modified 19 jul 2008