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

The exterior field of slowly and rapidly rotating neutron stars: Rehabilitating spacetime metrics involving hyperextreme objects