Note on the mass–radius relations for spherical compact objects in general relativity with semi-classical corrections

Abstract

We consider the effects that modifications to general relativity (GR) at high densities may have on the structure of spherical compact objects. Such effects can be modeled via semi-classical corrections that are manifest in an additional effective (i.e. non-physical) term in the energy momentum tensor. In particular, we consider two kinds of effective corrections that are quadratic in the density: one inspired by loop quantum gravity (LQG) and one inspired by Einstein– Cartan Theory (ECT). For both corrections, we consider two standard toy models of compact objects, one with polytropic equation of state and the other described by the MIT-bag model. We show that the LQG-inspired corrections can produce objects with greater radius and total mass, while the ECT-inspired corrections produce objects that are smaller and less massive than their counterparts in GR