Physica A 282 (2000) 203–211 www.elsevier.com/locate/physa Relativistic nonextensive kinetic theory Victor H. Hamity ∗ , Daniel E. Barraco Fa.M.A.F., Universidad Nacional de C ordoba, Ciudad Universitaria, C ordoba 5000, Argentina Received 16 December 1999 Abstract We present, in a coherent rigorous way, a generalization of the relativistic kinetic theory of par- ticles that includes the monoparametric (parameter q) family of thermal equilibrium distributions of Tsallis thermostatistics. The q-depending entropy function leads to a local distribution func- tion with a well-dened generalized temperature (not depending on q) but with other quantities such as the energy density, pressure, particle number density, etc., depending on q. In general, this extension forms the basis for relativistic thermodynamics of equilibrium and nonequilib- rium transport processes that includes nonextensivity. Astrophysics and cosmology are two of the areas where Tsallis’ theory may nd important applications. This is due to the nonextensive thermodynamical behaviour associated with the long range of gravitational interaction. Thus, a relativistic nonextensive kinetic theory may be appropriate for the treatment of a number of real systems, like the system of galaxies, hot gases of particles and plasmas. Also, it may be used to study a number of interesting problems in cosmology, like, for instance, the distribution of bubbles sizes, and consequently the level of inhomogeneity generated, in a scalar-tensor theory of gravity, as well as to apply it to another constituents, if we could extend the known history of the universe back to quark= hadron transition and electroweak phase transition. c  2000 Elsevier Science B.V. All rights reserved. PACS: 05.20.Dd; 05.30.−d; 05.90.+m Keywords: Nonextensivity; Cosmology; Gravitation 1. Introduction Our current understanding of the evolution of the Universe is based upon the Friedmann–Robertson–Walker cosmological model. This model has become known as the standard cosmology. Direct evidence supporting its validity, along with a kinetic theory model for the matter, extends back to the beginning of the epoch of primordial * Corresponding author. E-mail address: hamity@s.uncor.edu (V.H. Hamity) 0378-4371/00/$ - see front matter c  2000 Elsevier Science B.V. All rights reserved. PII: S0378-4371(00)00062-5