On the lowest energy state of a collisionless self-gravitating system under phase space volume constraints.
Abstract
The problem of minimizing the energy of a collisionless self-gravitating system under the only constraint of phase space volume conservation is reconsidered. With respect to the recent paper on the same subject by Wiechen, Ziegler and Schindler, the author brings about essentially three new results: 1. he establishes a lower bound on the energy by using arguments which are both simpler and more general than those of these authors; 2. he proves that the lowest energy state is necessarily spherically symmetric (in the physical space), and 3. he shows that, if one fixes also the total angular momentum J of the system, then there is no lowest energy state satisfying this further constraint if J ≠ 0.
- Publication:
-
Monthly Notices of the Royal Astronomical Society
- Pub Date:
- November 1989
- DOI:
- 10.1093/mnras/241.1.15
- Bibcode:
- 1989MNRAS.241...15A
- Keywords:
-
- Computational Astrophysics;
- Cosmology;
- Evolution (Development);
- Gravitation Theory;
- Angular Momentum;
- Integral Equations;
- Kinetic Energy;
- Potential Energy;
- Astrophysics;
- Stellar Systems: Gravitation