RELATIVISTIC STARS IN f (R) GRAVITY

We study the strong gravity regime in viable models of so-called f(R) gravity that account for the observed cosmic acceleration. Using a relaxation algorithm, we construct numerically static relativistic stars for a polytropic equation of state. We can reach a gravitational potential up to Φ ~ 0.3 at the surface of the star, even in f(R) theories with an “unprotected” curvature singularity. However, we find static configurations only if the pressure does not exceed one third of the energy density, except possibly in a limited region of the star (otherwise, one expects tachyonic instabilities to develop). This constraint is satisfied by realistic equations of state for neutron stars.