An all-purpose metric for the exterior of any kind of rotating neutron star

Abstract

We have tested the appropriateness of two-soliton analytic metric to describe the exterior of all types of neutron stars, no matter what their equation of state or rotation rate is. The particular analytic solution of the vaccuum Einstein equations proved quite adjustable to mimic the metric functions of all numerically constructed neutron-star models that we used as a testbed. The neutron-star models covered a wide range of stiffness, with regard to the equation of state of their interior, and all rotation rates up to the maximum possible rotation rate allowed for each such star. Apart of the metric functions themselves, we have compared the radius of the innermost stable circular orbit $R_{\rm{ISCO}}$, the orbital frequency $Ω\equiv\frac{dϕ}{dt}$ of circular geodesics, and their epicyclic frequencies $Ω_ρ, Ω_z$, as well as the change of the energy of circular orbits per logarithmic change of orbital frequency $Δ\tilde{E}$. All these quantities, calculated by means of the two-soliton analytic metric, fitted with good accuracy the corresponding numerical ones as in previous analogous comparisons (although previous attempts were restricted to neutron star models with either high or low rotation rates). We believe that this particular analytic solution could be considered as an analytic faithful representation of the gravitation field of any rotating neutron star with such accuracy, that one could explore the interior structure of a neutron star by using this space-time to interpret observations of astrophysical processes that take place around it.