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.Comment: Phys.Rev. D published, typos corrected to match the published versio
