1010.1271 (Andrew J. S. Hamilton)
Andrew J. S. Hamilton
(Abridged) A solution is obtained for the interior structure of an uncharged
rotating black hole that accretes a collisionless fluid. The solution is
conformally stationary, axisymmetric, and conformally separable, possessing a
conformal Killing tensor. Hyper-relativistic counter-streaming between
collisionless ingoing and outgoing streams drives inflation at (just above) the
inner horizon, followed by collapse. As ingoing and outgoing streams approach
the inner horizon, they focus into twin narrow beams directed along the ingoing
and outgoing principal null directions, regardless of the initial angular
motions of the streams. The radial energy-momentum of the counter-streaming
beams gravitationally accelerates the streams even faster along the principal
directions, leading to exponential growth in the streaming density and
pressure, and in the Weyl curvature and mass function. At exponentially large
density and curvature, inflation stalls, and the spacetime collapses. As the
spacetime collapses, the angular motions of the freely-falling streams grow.
When the angular motion has become comparable to the radial motion, which
happens when the conformal factor has shrunk to an exponentially tiny scale,
conformal separability breaks down, and the solution fails. The condition of
conformal separability prescribes the form of the ingoing and outgoing
accretion flows incident on the inner horizon. The dominant radial part of the
solution holds provided that the densities of ingoing and outgoing streams
incident on the inner horizon are uniform, independent of latitude; that is,
the accretion flow is "monopole." The sub-dominant angular part of the solution
requires a special non-radial pattern of angular motion of streams incident on
the inner horizon. The prescribed angular pattern cannot be achieved if the
collisionless streams fall freely from outside the horizon.
View original:
http://arxiv.org/abs/1010.1271
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