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Rapidly rotating neutron stars in scalar-tensor theories of gravity

We present the field equations governing the equilibrium of rapidly rotating neutron stars in scalar-tensor theories of gravity, as well as representative numerical solutions. The conditions for the presence of a nontrivial scalar field and the deviations from the general relativistic solutions are studied. Two examples of scalar-tensor theories are examined - one case that is equivalent to the Brans-Dicke theory and a second case, that is perturbatively equivalent to Einstein's General Relativity in the weak field regime, but can differ significantly for strong fields. Our numerical results show that rapidly rotating neutron star models with a nontrivial scalar field exist in both cases and that the effect of the scalar field is stronger for rapid rotation. If we consider values of the coupling parameters in accordance with current observations, only the second example of scalar-tensor theories has significant influence on the neutron star structure. We show that scalarized, rapidly rotating neutron stars exist for a larger range of the parameters than in the static case, since a nontrivial scalar field is present even for values of the coupling constant $β>-4.35$, and that these solutions are energetically more favorable than the general relativistic ones. In addition, the deviations of the rapidly rotating scalar-tensor neutron stars from the general-relativistic solutions is significantly larger than in the static case.