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Advances in High Energy Physics
Volume 2016 (2016), Article ID 2601741, 8 pages
http://dx.doi.org/10.1155/2016/2601741
Research Article

On the Jeans Theorem and the “Tolman–Oppenheimer–Volkoff Equation” in Gravity

1Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, OK 73019, USA
2International Institute for Applicable Mathematics & Information Sciences (IIAMIS), Hyderabad, India
3International Institute for Applicable Mathematics & Information Sciences (IIAMIS), Udine, Italy
4G. P. Birla Observatory & Astronomical Research Centre, B. M. Birla Science Centre, Adarsh Nagar, Hyderabad 500 063, India
5Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), P.O. Box 55134-441, Maragha, Iran

Received 14 June 2016; Revised 31 August 2016; Accepted 15 September 2016

Academic Editor: Burak Bilki

Copyright © 2016 Rishabh Jain et al. 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. The publication of this article was funded by SCOAP3.

Abstract

Corda, Mosquera Cuesta, and Lorduy Gòmez have shown that spherically symmetric stationary states can be used as a model for galaxies in the framework of the linearized gravity. Those states could represent a partial solution to the Dark Matter Problem. Here, we discuss an improvement of this work. In fact, as the star density is a functional of the invariants of the associated Vlasov equation, we show that any of these invariants is in its turn a functional of the local energy and the angular momentum. As a consequence, the star density depends only on these two integrals of the Vlasov system. This result is known as the “Jeans theorem.” In addition, we find an analogy of the historical Tolman–Oppenheimer–Volkoff equation for the system considered in this paper. For the sake of completeness, in the final section of the paper, we consider two additional models which argue that Dark Matter could not be an essential element.