Mass bounds for compact spherically symmetric objects in generalized gravity theories

Abstract

We derive upper and lower bounds on the mass-radius ratio of stable compact objects in extended gravity theories, in which modifications of the gravitational dynamics via-{\' a}-vis standard general relativity are described by an effective contribution to the matter energy-momentum tensor. Our results include the possibility of a variable coupling between the matter sector and the gravitational field and are valid for a large class of generalized gravity models. The generalized continuity and Tolman-Oppenheimer-Volkoff equations are expressed in terms of the effective mass, density and pressure, given by the bare values plus additional contributions from the total energy-momentum tensor, and general theoretical limits for the maximum and minimum mass-radius ratios are explicitly obtained. As an applications of the formalism developed herein, we consider compact bosonic objects, described by scalar-tensor gravitational theories with self-interacting scalar field potentials, and charged compact objects, respectively. For Higgs type models, we find that these bounds can be expressed in terms of the value of the potential at the surface of the compact object. Minimizing the energy with respect to the radius, we obtain explicit upper and lower bounds on the mass, which admits a Chandrasekhar type representation. For charged compact objects, we consider the effects of the Poincar\'{e} stresses on the equilibrium structure and obtain bounds on the radial and tangential stresses. As a possible astrophysical test of our results, we obtain the general bound on the gravitational redshift for compact objects in extended gravity theories. General implications of minimum mass bounds for the gravitational stability of fundamental particles and for the existence of holographic duality between bulk and boundary degrees of freedom are also considered.