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 \beta > -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 .