What does a measurement of mass and/or radius of a neutron star   constrain: Equation of state or gravity?
  Neutron stars (NSs) are thought to be excellent laboratories for determining the equation of state (EoS) of cold dense matter. Their strong gravity suggests that they can also be used to constrain gravity models. The mass and radius (M-R) of a NS both depend on the choice of EoS and gravity, meaning that NSs cannot be simultaneously good laboratories for both of these questions. A measurement of M-R would constrain the less well known physics input. The assumption that M-R measurements can be used to constrain EoS-presumes general relativity (GR) is the ultimate model of gravity in the classical regime. We calculate the radial profile of compactness and curvature (square root of the full contraction of the Weyl tensor) within a NS and determine the domain not probed by the Solar System tests of GR. We find that, except for a tiny sphere of radius less than a millimeter at the center, the curvature is several orders of magnitude above the values present in Solar System tests. The compactness is beyond the solar surface value for r>10 m, and increases by 5 orders of magnitude towards the surface. With the density being only an order of magnitude higher than that probed by nuclear scattering experiments, our results suggest that the employment of GR as the theory of gravity describing the hydrostatic equilibrium of NSs is a rather remarkable extrapolation from the regime of tested validity, as opposed to that of EoS models. Our larger ignorance of gravity within NSs suggests that a measurement of M-R constrains gravity rather than EoS, and given that EoS has yet to be determined by nucleon scattering experiments, M-R measurements cannot tightly constrain the gravity models either. Near the surface the curvature and compactness attain their largest values, while EoS in this region is fairly well known. This renders the crust as the best site to look for deviations from GR. 
Kazim Yavuz Ek\c{s}i, Can G\"ung\"or, Murat Metehan T\"urko\u{g}lu
astro-ph.HE gr-qc