Eur. Phys. J. B 43, 143-154 (2005)
https://doi.org/10.1140/epjb/e2005-00037-3

Mean field theory and geodesics in general relativity

ERGA, UMR 8112, 4 Place Jussieu, 75231 Paris Cedex 05, France

Corresponding author: ^a fabrice.debbasch@wanadoo.fr

Received: 5 May 2004
Revised: 27 September 2004
Published online: 11 February 2005

Abstract

It is proven that all geodesics in a mean gravitational field can be interpreted locally as the averages of geodesics in the unaveraged field. The respective time-like, space-like or null character of averaged and unaveraged geodesics is discussed carefully. Finally, some important astrophysical and cosmological applications and consequences are investigated.