Eur. Phys. J. B (2012) 85: 360
https://doi.org/10.1140/epjb/e2012-30357-x

Regular Article

Density distribution for an inhomogeneous finite gravitational system

¹ Serampore College, Serampore, Hooghly, West Bengal, India
² Saha Institute of Nuclear Physics, I/AF Bidhannagar, 700064 Calcutta, India

^a e-mail: ms.janaki@saha.ac.in

Received: 2 May 2012
Received in final form: 9 August 2012
Published online: 29 October 2012

Abstract

An attempt is made to develop an equilibrium kinetic equation for a weakly non ideal inhomogeneous gravitational system utilizing the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations. It is shown that the pair correlational function explicitly depends upon the nature of binary interaction between particles. The corresponding kinetic equation containing pair correlation corrections is devoid of the degeneracy present in the collisionless Boltzmann equation with respect to the nature of the two particle interactions, unlike the Vlasov equation that cannot recognize the nature of two particle interaction. A net effect of the particle correlations can be realized only if the spatial symmetry of the correlation interaction is broken due to a spatial inhomogeneity. Such an inhomogeneity is inherently present in a bulk gravitational system in view of the unshielded long range nature of the two-particle interactions. In a finite gravitational system, the effects of pair correlations in the first order kinetic equation can be expressed in terms of the macroscopic gravitational potential to obtain a modified Boltzmann distribution that includes the effects of correlations.