Statistical mechanics and the gravothermal catastrophe.
Abstract
Jensen's inequality is applied to the canonical partition function of a self-gravitating system to determine the best independent particle potential. The inequality allows the stability to be analyzed very easily. We recover the results of Lynden-Bell and Wood for the onset of an instability in an isothermal sphere in a heat bath. Our eigenvalue analysis leads to results very similar to those of Horwitz and Katz, but we differ in the description of the l=1 perturbation.
- Publication:
-
Journal of Mathematical Physics
- Pub Date:
- 1981
- DOI:
- 10.1063/1.524886
- Bibcode:
- 1981JMP....22..348C
- Keywords:
-
- Relativistic Astrophysics;
- Gravitation Theory;
- Background Radiation;
- Black Holes