Compact objects in quadratic Palatini gravity generated by a free scalar field

We study the correspondence that connects the space of solutions of General Relativity (GR) with that of Ricci-based Gravity theories (RBGs) of the $f(R,Q)$ type in the metric-affine formulation, where $Q=R_{(\mu\nu)}R^{(\mu\nu)}$. We focus on the case of scalar matter and show that when one considers a free massless scalar in the GR frame, important simplifications arise that allow to establish the correspondence for arbitrary $f(R,Q)$ Lagrangian. We particularize the analysis to a quadratic $f(R,Q)$ theory and use the spherically symmetric, static solution of Jannis-Newman-Winicour as seed to generate new compact objects in our target theory. We find that two different types of solutions emerge, one representing naked singularities and another corresponding to asymmetric wormholes with bounded curvature scalars everywhere. The latter solutions, nonetheless, are geodesically incomplete.