Geodesic
The space-times symmetries and equilibrium distributions of the charged fluids. The equations of the state
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 148 (2006) no. 3, pp. 49-64 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Space-times $V_4$, admittings a groups of homothetic motions $H_r$ with charged fluid as its source are discussed. It is assumed that the vector of macroscopic velocity of the fluid is collinear to the time-like vector $\mathbf Y=\xi^i \partial_i$ of the group's Lie algebra. We prove that if $(\rho+p)\neq 0$, the vector $\mathbf Y$ is the vector of the Lie algebra, corresponding to isometric transformations of the group $H_r$ and giving rise to time-like ideal of the Lie algebra of the group $H_r$. All space-times $V_4$, admitting a groups of homothetic transformations with indicated properties, are selected. Equations $(T^{ik}+E^{ik})_{|k}=0$ are integrated entirely, and all possible equations of state of investigated fluid are presented. It is founded that equation of state of the fluid practically uniquely fixed by the space-time's symmetry and pressure, energy density as well as electrical charges expressed solely through “field” quantities: $A_k\xi^k $ and $\xi_k\xi^k$, where $A_k$ is the 4-potential of an electromagnetic field. 
@article{UZKU_2006_148_3_a3,
     author = {R. A. Daishev},
     title = {The space-times symmetries and equilibrium distributions of the charged fluids. {The} equations of the state},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {49--64},
     year = {2006},
     volume = {148},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2006_148_3_a3/}
}
TY  - JOUR
AU  - R. A. Daishev
TI  - The space-times symmetries and equilibrium distributions of the charged fluids. The equations of the state
JO  - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
PY  - 2006
SP  - 49
EP  - 64
VL  - 148
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/UZKU_2006_148_3_a3/
LA  - ru
ID  - UZKU_2006_148_3_a3
ER  - 
%0 Journal Article
%A R. A. Daishev
%T The space-times symmetries and equilibrium distributions of the charged fluids. The equations of the state
%J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
%D 2006
%P 49-64
%V 148
%N 3
%U http://geodesic.mathdoc.fr/item/UZKU_2006_148_3_a3/
%G ru
%F UZKU_2006_148_3_a3
R. A. Daishev. The space-times symmetries and equilibrium distributions of the charged fluids. The equations of the state. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 148 (2006) no. 3, pp. 49-64. http://geodesic.mathdoc.fr/item/UZKU_2006_148_3_a3/

[1] Chernikov N.A., Relyativistskii gaz v gravitatsionnom pole, Preprint No 1027, OIYaI, Dubna, 1962

[2] Chernikov N. A., Ravnovesnoe raspredelenie relyativistskogo gaza, Preprint No 1159, OIYaI, Dubna, 1962

[3] Stewart J. M., Non-equilibrium relativistic kinetic theory, Springer-Verlag, Berlin, 1971

[4] Zimdahl W., Triginer J., Pavon D., “Collisional equilibrium, particle production, and the inflationary universe”, Phys. Rev. D, 54:10 (1996), 6101–6110 | DOI | MR

[5] Zimdahl W., “Reacting fluids in the expanding universe: a new mechanism for entropy production”, Mon. Not. R. Astron. Soc., 288:3 (1997), 665–673

[6] Zimdahl W., “Cosmological particle production and generalized thermodynamic equilibrium”, Phys. Rev. D, 57:4 (1998), 2245–2254 | DOI | MR

[7] Daishev R. A., Zimdahl W., “On homothetic cosmological dynamics”, Class. Quantum Grav., 20:23 (2003), 5017–5024 | DOI | MR

[8] Burd A., Coley A. A., “Viscous fluid cosmology”, Class. Quantum Grav., 11:1 (1994), 83–105 | DOI | MR | Zbl

[9] Carr B. J., Coley A. A., “Self-similarity in general relativity”, Class. Quantum Grav., 16:7 (1999), R31–R71 | DOI | MR | Zbl

[10] Carot J., Sintes A. M., “Homothetic perfect fluid space-times”, Class. Quantum Grav., 14:5 (1997), 1183–1205 | DOI | MR | Zbl

[11] Daishev R. A., Karin V. A., “Ravnovesnye raspredeleniya zaryazhennoi zhidkosti v prostranstvakh-vremenakh s prostotranzitivnymi gruppami gomoteticheskikh dvizhenii”, Uch. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 148, kn. 2 (2006), 37–53 | Zbl

[12] Wainright J., Yaremovicz P. A. E., “Killing vector fields and Eistein–Maxwell field equations with perfect-fluid source”, Gen. Rel. Grav., 7:4 (1976), 345–359 | MR

[13] Petrov A. Z., Novye metody v obschei teorii otnositelnosti, Nauka, M., 1966, 495 pp. | MR

[14] Knebelman M. S., “Homothetic mappings of the Riemann spaces”, Proc. Amer. Math. Soc., 9:6 (1958), 926–927 | DOI | MR

[15] Daishev R. A., “Odnorodnye resheniya uravnenii Einshteina s idealnoi zaryazhennoi zhidkostyu”, Izv. vuzov. Fizika, 1984, no. 12, 74–79