Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bar mode instability in relativistic rotating stars: a post Newtonian
  treatment   We construct analytic models of incompressible, rigidly rotating stars in PN
gravity and study their stability against nonaxisymmetric Jacobi-like bar
modes. PN configurations are modeled by homogeneous triaxial ellipsoids and the
metric is obtained as a solution of Einstein's equations in 3+1 ADM form. We
use an approximate subset of the equations well-suited to numerical integration
for strong field, 3D configurations in quasi--equilibrium. These equations are
exact at PN order, and admit an analytic solution for homogeneous ellipsoids.
In this paper we present this solution, as well as analytic functionals for the
conserved global quantities, M, M_0 and J. By using a variational principle we
construct sequences of axisymmetric equilibria of constant density and rest
mass, i.e. the PN generalization of Maclaurin spheroids, which are compared to
other PN and full relativistic sequences presented by previous authors. We then
consider nonaxisymmetric ellipsoidal deformations of the configurations,
holding J constant and the rotation uniform, and we locate the point at which
the bar modes will be driven secularly unstable by a dissipative agent like
viscosity. We find that the value of the eccentricity, as well as the ratios
\Omega^2/(\pi\rho_0) and T/|W|, defined invariantly, all increase at the onset
of instability as the stars become more relativistic. Since higher degrees of
rotation are required to trigger a viscosity-driven bar mode as the star's
compactness increases, the effect of GR is to weaken the instability, at least
to PN order. This behavior is opposite to that found for secular instability
via Dedekind-like modes driven unstable by gravitational radiation, supporting
the suggestion that in GR, nonaxisymmetric modes driven unstable by viscosity
and gravitational radiation may no longer coincide.

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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: nlin