General relativistic rotating boson stars were later found [193, 222] with the same ansatz of
Eq. (67). To obtain stationary axially symmetric solutions, two symmetries were imposed on the
spacetime described by two commuting Killing vector fields
and
in a system of
adapted (cylindrical) coordinates
. In these coordinates, the metric is independent
of
and
and can be expressed in isotropic coordinates in the Lewis–Papapetrou form
The entire family of solutions for and part of
was computed using the self-consistent
field method [222], obtaining a maximum mass
. Both families were completely
computed in [141] using faster multigrid methods, although there were significant discrepancies in the
maximum mass, which indicates a problem with the regularity condition on the z-axis. The mass
and
angular momentum
for stationary asymptotically flat spacetimes can be obtained from their respective
Komar expressions. They can be read off from the asymptotic expansion of the metric functions
and
Recently, their stability properties were found to be similar to nonrotating stars [135]. Rotating boson
stars have been shown to develop a strong ergoregion instability when rapidly spinning on short
characteristic timescales (i.e., 0.1 seconds – 1 week for objects with mass
and angular
momentum
), indicating that very compact objects with large rotation are probably black
holes [44].
More discussion concerning the numerical methods and limitations of some of these approaches can be found in Lai’s PhD thesis [141].
http://www.livingreviews.org/lrr-2012-6 |
Living Rev. Relativity 15, (2012), 6
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