Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of rigidly rotating supermassive stars against gravitational
  collapse   We revisit secular stability against quasi-radial collapse for rigidly
rotating supermassive stars (SMSs) in general relativity. We suppose that the
SMSs are in a nuclear-burning phase and can be modeled by polytropic equations
of state with the polytropic index $n_p$ slightly smaller than $3$. The
stability is determined in terms of the turning-point method. We find a fitting
formula of the stability condition for the plausible range of $n_p$ ($2.95 \alt
n_p \alt 3$) for SMSs. This condition reconfirms that, while non-rotating SMSs
with mass $\sim 10^5M_\odot$--$10^6M_\odot$ may undergo a
general-relativistically induced quasi-radial collapse, rigidly rotating SMSs
with a ratio of rotational to gravitational potential energy ($\beta$) of $\sim
10^{-2}$ are likely to be stable against collapse unless they are able to
accrete $\sim 5$ times more mass during the (relatively brief) hydrogen-burning
phase of their evolution. We discuss implications of our results.

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The categories of this paper are: cond-mat
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con