**AAS 200th meeting, Albuquerque, NM, June 2002**

*Session 80. Neutron Stars, Relativity, MHO*

Oral, Thursday, June 6, 2002, 10:00-11:30am, San Miguel
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## [80.04D] Relativistic Self-similar Equilibria and Non-axisymmetric Neutral Modes

*Mike J. Cai, F. H. Shu (U. C. Berkeley)*

We have constructed semi-analytic axisymmetric scale free
solutions to Einstein field equations with perfect fluid
matter source. These spacetimes are self-similar under the
simultaneous transformation r'= ar and t'=a^{1-n}t. We
explored the two dimensional solution space parameterized by
the rescaling index n and the isothermal sound speed
\gamma^{1/2}. The isopycnic surfaces are in general
toroids. As the equilibrium configuration rotates faster, an
ergo region develops in the form of the exterior of a cone
centered about the symmetry axis. The sequence of solution
terminates when frame dragging becomes infinite and the ergo
cone closes onto the axis. In the extreme flattening limit,
we have also searched for non-axisymmetric neutral modes in
a self-similar disk. Two separate sets of tracks are
discovered in the solution space. One corresponds to the
bifurcation points to non-axisymmetric equilibria, which is
confined in the non-ergo solutions. The other track signals
the onset of instability driven by gravitational radiation.
These solutions are formally infinite in extent, and thus
can not represent realistic astrophysical systems. However,
if these properties do not alter qualitatively when the
self-similar configurations are truncated, then these
solutions may serve as initial data for dynamic collapse in
super massive black hole formation.

The author(s) of this abstract have provided an email address
for comments about the abstract:
mcai@astron.berkeley.edu

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Bulletin of the American Astronomical Society, **34**

© 2002. The American Astronomical Soceity.