Kinetic equation for a weakly relativistic system with gravitational interaction
Teoretičeskaâ i matematičeskaâ fizika, Tome 27 (1976) no. 2, pp. 262-266
Cet article a éte moissonné depuis la source Math-Net.Ru
Kinetic equations of the type of those of Vlasov and Landau are obtained for systems with gravitational interaction by the use of the weakly relativistic BBGKY hierarchy. Allowance is made for the $\varepsilon$ and $\varepsilon^2$ orders of magnitude in the dimensionless coupling constant $\varepsilon$. It is shown that the collision integral in the weakly relativistic Landau equation vanishes identically when the momentum distribution function $A(1-p^2/m^2c^2)\times\exp(-\gamma p^2-3\gamma p^4/4m^3c^2)$ is substituted. Here, $A$ and $\gamma$ are constants, $c$ is the velocity of light, $m$ is the rest mass of the particle, $\mathbf p=m(d\mathbf q/dt)$, $\mathbf q$, is the coordinate of the particle, and $t$ is the time of an observer in an inertial frame of reference.
@article{TMF_1976_27_2_a14,
author = {L. G. Shekhovtsova},
title = {Kinetic equation for a~weakly relativistic system with gravitational interaction},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {262--266},
year = {1976},
volume = {27},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1976_27_2_a14/}
}
L. G. Shekhovtsova. Kinetic equation for a weakly relativistic system with gravitational interaction. Teoretičeskaâ i matematičeskaâ fizika, Tome 27 (1976) no. 2, pp. 262-266. http://geodesic.mathdoc.fr/item/TMF_1976_27_2_a14/
[1] D. ter Haar, G. Wergeland, Phys. Lett., 1C (1971), 31 | Zbl
[2] I. P. Pavlotskii, DAN SSSR, 188 (1969), 784
[3] A. A. Baranov, E. T. Bruk-Levinson, I. P. Pavlotskii, L. G. Shekhovtseva, DAN BSSR, XVII (1973), 801
[4] N. N. Bogolyubov, Izbrannye trudy, t. II, «Naukova dumka», Kiev, 1970 | MR
[5] F. Jüttner, Ann. Phys., 34 (1911), 856 | DOI | Zbl
[6] N. A. Chernikov, Preprint OIYaI R-1159, Dubna, 1962