Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Critical gravitational collapse with angular momentum II: soft equations
  of state   We study critical phenomena in the collapse of rotating ultrarelativistic
perfect fluids, in which the pressure $P$ is related to the total energy
density $\rho$ by $P=\kappa\rho$, with $\kappa$ a constant. We generalize
earlier results for radiation fluids with $\kappa=1/3$ to other values of
$\kappa$, focussing on $\kappa < 1/9$. For $1/9<\kappa \lesssim 0.49$, the
critical solution has only one unstable, growing mode, which is spherically
symmetric. For supercritical data it controls the black hole mass, while for
subcritical data it controls the maximum density. For $\kappa<1/9$, an
additional axial $l=1$ mode becomes unstable. This controls either the black
hole angular momentum, or the maximum angular velocity. In theory, the
additional unstable $l=1$ mode changes the nature of the black hole threshold
completely: at sufficiently large initial rotation rates $\Omega$ and
sufficient fine-tuning of the initial data to the black hole threshold we
expect to observe nontrivial universal scaling functions (familiar from
critical phase transitions in thermodynamics) governing the black hole mass and
angular momentum, and, with further fine-tuning, eventually a finite black hole
mass almost everywhere on the threshold. In practice, however, the second
unstable mode grows so slowly that we do not observe this breakdown of scaling
at the level of fine-tuning we can achieve, nor systematic deviations from the
leading-order power-law scalings of the black hole mass. We do see systematic
effects in the black-hole angular momentum, but it is not clear yet if these
are due to the predicted non-trivial scaling functions, or to nonlinear effects
at sufficiently large initial angular momentum (which we do not account for in
our theoretical model).

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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: math
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: nlin