Abstract:
We investigate the properties of a closed-form analytic solution
recently
found by Manko et al. (2000) for the exterior spacetime of
rapidly
rotating neutron stars. For selected equations of state we
numerically
solve the full Einstein equations to determine the neutron star
spacetime
along constant rest mass sequences. The analytic solution is then
matched
to the numerical solutions by imposing that the quadrupole moment of
the
numerical and analytic spacetimes be the same. For the analytic
solution
we consider, such a matching condition can be satisfied only for very
rapidly
rotating stars. When solutions to the matching condition exist, they
belong
to one of two branches. For one branch the current octupole
moment
of the analytic solution is very close to the current octupole moment
of
the numerical spacetime; the other branch is more similar to the Kerr
solution.
We present an extensive comparison of the radii of innermost stable
circular
orbits (ISCO) obtained with a) the analytic solution, b) the Kerr
metric,
c) an analytic series expansion derived by Shibata and Sasaki (1998)
and
d) a highly accurate numerical code. In most cases where a corotating
ISCO
exists, the analytic solution has an accuracy consistently better than
the
Shibata-Sasaki expansion. The numerical code is used for tabulating the
mass-quadrupole
and current-octupole moments for several sequences of constant rest
mass.
UPDATE:
Leonardo Pachón kindly sent us a mathematic notebook for a new
6-parameter solution by Pachón, Rueda & Sanabria-Gómez,
PRD
73, 104038 (2006) . You can download the original file, as sent
to us by L. Pachón,
here.