Performing tests of strong-field gravity with neutron stars requires knowledge of the equation of state of
neutron-star matter to a degree better than the required precision of the gravitational test. This appears
from the outset to be a serious hurdle given the wide range of predictions of equally plausible theories of
neutron-star matter (see [83] for a recent compilation). It is easy to show, however, that current
uncertainties in our modeling of the properties of ultra-dense matter do not preclude significant constraints
on the strong-field behavior of gravity [43].
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During the last three decades, neutron-star models have been calculated for a variety of gravity theories
(see [180] and references therein) and were invariably different, both in size and in allowed mass, than
their general relativistic counterparts. As an example, Figure 13 shows neutron-star models
calculated in three representative theories that cannot be excluded by current tests that do
not involve neutron stars. In the figure, the shaded areas represent the uncertainty introduced
by the unknown equation of state of neutron-star matter (not including quark stars or large
neutron stars with condensates). Clearly, the deviations in neutron-star properties from the
predictions of general relativity for these theories (that are still consistent with weak-field tests)
are larger than the uncertainty introduced by the unknown equation of state of neutron-star
matter.
This is a direct consequence of the fact that the curvature around a neutron star is larger by
13 orders of magnitude compared to the curvature probed by solar-system tests, whereas
the density inside the neutron star is larger by only an order of magnitude compared to the
densities probed by nuclear scattering data that are used to constrain the equation of state. Given
that the current values of the post-Newtonian parameters are known from weak-field tests to
within
10–5, it is reasonable that deviations from general relativity can be hidden in the
weak-field limit but may become dominant as the curvature is increased by more than ten orders of
magnitude. Neutron stars can indeed be used in testing the strong-field behavior of a gravity
theory.
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