On neutron stars in ƒ (R) theories: Small radii, large masses and large energy emitted in a merger

In the context of ƒ (R) gravity theories, we show that the apparent mass of a neutron star as seen from an observer at infinity is numerically calculable but requires careful matching, first at the star’s edge, between interior and exterior solutions, none of them being totally Schwarzschild-like but presenting instead small oscillations of the curvature scalar R; and second at large radii, where the Newtonian potential is used to identify the mass of the neutron star. We find that for the same equation of state, this mass definition is always larger than its general relativistic counterpart. We exemplify this with quadratic R^2 and Hu-Sawicki-like modifications of the standard General Relativity action. Therefore, the finding of two-solar mass neutron stars basically imposes no constraint on stable ƒ (R) theories. However, star radii are in general smaller than in General Relativity, which can give an observational handle on such classes of models at the astrophysical level. Both larger masses and smaller matter radii are due to much of the apparent effective energy residing in the outer metric for scalar-tensor theories. Finally, because the ƒ (R) neutron star masses can be much larger than General Relativity counterparts, the total energy available for radiating gravitational waves could be of order several solar masses, and thus a merger of these stars constitutes an interesting wave source.