Spherical symmetric solutions of conformal Killing gravity: black holes, wormholes, and sourceless cosmologies

The most general set of static and spherically symmetric solutions for conformal Killing gravity coupled to Maxwell fields is presented in closed form. These solutions, depending on six parameters, include non-asymptotically flat black holes or naked singularities, non-asymptotically flat traversable wormholes, and (possibly singularity-free) closed universes. We also consider the inverse problem, showing that the most general energy-momentum tensor generating a given static spherically symmetric metric depends on three parameters. Sourceless time-dependent isotropic solutions are also given. These solutions depending on the curvature, the cosmological constant, and a new integration constant $\alpha$, present a rich variety, including singularity-free eternal cosmologies and universes evolving symmetrically from a big bang to a big crunch within a finite lapse of time.