  In recent years, a lot of work was done that has revealed some very
interesting properties of neutron stars. One can relate the first few multipole
moments of a neutron star, or quantities that can be derived from them, with
relations that are independent of the equation of state (EoS). This is a very
significant result that has great implications for the description of neutron
stars and in particular for the description of the spacetime around them.
Additionally, it was recently shown that there is a four parameter analytic
spacetime, known as the two-soliton spacetime, which can accurately capture the
properties of the geometry around neutron stars. This allows for the
possibility of describing in a unified formalism the astrophysically relevant
properties of the spacetime around a neutron star independently of the
particulars of the EoS for the matter of the star. More precisely, the
description of these astrophysical properties is done using an EoS omniscient
spacetime that can describe the exterior of any neutron star. In the present
work we investigate properties such as the location of the innermost stable
circular orbit $R_{ISCO}$ (or the surface of the star when the latter overcomes
the former), the various frequencies of perturbed circular equatorial
geodesics, the efficiency of an accretion disc, its temperature distribution,
and other properties associated with the emitted radiation from the disc, in a
way that holds for all possible choices of a realistic EoS for the neutron
star. Furthermore, we provide proof of principle that if one were to measure
the right combinations of pairs of these properties, with the additional
knowledge of the mass of the neutron star, one could determine the EoS of the
star.
