The gravitational field of a star in quadratic gravity

The characterization of the gravitational field of isolated objects is still an open question in quadratic theories of gravity. We study static equilibrium solutions for a self-gravitating fluid in extensions of General Relativity including terms quadratic in the Weyl tensor and in the Ricci scalar. We parametrize the external field in terms of the total mass and the strength of two Yukawa corrections associated with the quadratic terms in the action. Depending on the value of the mass-ratio of the two massive propagating degrees of freedom, these corrections are completely determined by the mass and the radius of the star. At variance with classical General Relativity, measurable definitions of the mass-energy of a star are not uniquely determined by its ADM mass, on the contrary distinct quasi-local definitions should be used to properly characterize the external field. We suggest that this apparent ambiguity can conveniently be exploited to detect deviations from standard General Relativity.