  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.
