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6 Current Tests of Strong-Field Gravity with Neutron Stars

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 [43Jump To The Next Citation Point].

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Figure 13: Mass-radius relations of neutron stars in general relativity (GR), scalar-tensor gravity (ST), and Rosen’s bimetric theory of gravity [43Jump To The Next Citation Point]. The shaded areas represent the range of mass-radius relations predicted in each case by neutron-star equations of state without unconfined quarks or condensates. All gravity theories shown in the figure are consistent with solar-system tests but introduce variations in the predicted sizes of neutron stars that are significantly larger than the uncertainty caused by the unknown equation of state.

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 13View Image 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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Figure 14: The limiting rate for the evolution of the orbital periods (τ−P1 ≡ P˙∕P) of five known millisecond, accreting pulsars as a function of the Brans–Dicke parameter ω BD. The lower half of the plot corresponds to an orbital period that decreases with time (˙ P∕P < 0), whereas the upper half corresponds to an orbital period that increases with time (P˙∕P > 0). Only the area outside the two curves for each system is physically allowed [125Jump To The Next Citation Point].
 6.1 Brans–Dicke gravity and the orbital decay of binary systems with neutron stars
 6.2 Second-order scalar-tensor gravity and radio pulsars
 6.3 Second-order scalar-tensor gravity and X-ray observations of accreting neutron stars

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