

The exterior metric of a rapidly rotating neutron star differs
considerably from the Kerr metric. The two metrics agree only to
lowest order in the rotational velocity [149]. At higher order, the multipole moments of the gravitational
field created by a rapidly rotating compact star are different
from the multipole moments of the Kerr field. There have been
many attempts in the past to find analytic solutions to the
Einstein equations in the stationary, axisymmetric case, that
could describe a rapidly rotating neutron star. An interesting
solution has been found recently by Manko
et al.
[220,
221]. For non-magnetized sources of zero net charge, the solution
reduces to a 3-parameter solution, involving the mass, specific
angular momentum, and a parameter that depends on the quadrupole
moment of the source. Although this solution depends explicitly
only on the quadrupole moment, it approximates the gravitational
field of a rapidly rotating star with higher nonzero multipole
moments. It would be interesting to determine whether this
analytic quadrupole solution approximates the exterior field of a
rapidly rotating star more accurately than the quadrupole,
, slow rotation approximation.
The above analytic solution and an earlier one that was not
represented in terms of rational functions [219] have been used in studies of energy release during disk
accretion onto a rapidly rotating neutron star [279
,
280
]. In [276
], a different approximation to the exterior spacetime, in the
form of a multipole expansion far from the star, has been used to
derive approximate analytic expressions for the location of the
innermost stable circular orbit (ISCO). Even though the analytic
solutions in [276
] converge slowly to an exact numerical solution at the surface
of the star, the analytic expressions for the location and
angular velocity at the ISCO are in good agreement with numerical
results.


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Rotating Stars in Relativity
Nikolaos Stergioulas
http://www.livingreviews.org/lrr-2003-3
© Max-Planck-Gesellschaft. ISSN 1433-8351
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