Exact solutions in ${\mathcal{R}}^2$ SUGRA

This letter is devoted to show that the bosonic sector of the ${\mathcal{R}}^2$-SUGRA in four dimensions, constructed with the F-term, admits a variety of exact and analytic solutions which include, pp- and AdS waves, asymptotically flat and AdS black holes and wormholes, as well as product spacetimes. The existence of static black holes and wormholes implies that a combination involving the Ricci scalar plus the norm of the field strength of the auxiliary two-form $B_{\mu \nu }$, must be a constant. We focus on this sector of the theory which has two subsectors depending on whether such a combination vanishes or not.