Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gravitational instability of isothermal and polytropic spheres   We complete previous investigations on the thermodynamics of self-gravitating
systems by studying the grand canonical, grand microcanonical and isobaric
ensembles. We also discuss the stability of polytropic spheres in the light of
a generalized thermodynamics proposed by Tsallis. We determine in each case the
onset of gravitational instability by analytical methods and graphical
constructions in the Milne plane. We also discuss the relation between
dynamical and thermodynamical stability of stellar systems and gaseous spheres.
Our study provides an aesthetic and simple approach to this otherwise
complicated subject.

13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg