  The 4-parameter exact solution presumably describing the exterior
gravitational field of a generic neutron star is presented in a concise
explicit form defined by only three potentials. In the equatorial plane, the
metric functions of the solution are found to be given by particularly simple
expressions that make them very suitable for the use in concrete applications.
Following Pappas and Apostolatos, we perform a comparison of the multipole
structure of the solution with the multipole moments of the known physically
realistic Berti-Stergioulas numerical models of neutron stars to argue that the
hyperextreme sectors of the solution are not less (but possibly even more)
important for the correct description of rapidly rotating neutron stars than
the subextreme sector involving exclusively the black-hole constituents. We
have also worked out in explicit form an exact analog of the well-known
Hartle-Thorne approximate metric.
