International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 3, Pages 591-597
doi:10.1155/S0161171284000636
A construction of the general relativistic Boltzmann equation
1Department of Mathematics, Imperial College, London S.W. 7, UK
2Euritanius 32, Athens 613, Greece
Received 4 December 1983
Copyright © 1984 P. Dolan and A. C. Zenios. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Our work depends essentially on the notion of a one-particle seven-dimensional state-space. In constructing a general relativistic theory we assume that all measurable quantities arise from invariant differential forms. In this paper, we study only the case when instantaneous, binary, elastic collisions occur between the particles of the gas. With a simple model for colliding particles and their collisions, we derive the kinetic equation, which gives the change of the distribution function along flows in state-space.