  Quadratic gravity constitutes a prototypical example of a perturbatively
renormalizable quantum theory of the gravitational interactions. In this work,
we construct the associated phase space of static, spherically symmetric, and
asymptotically flat spacetimes. It is found that the Schwarzschild geometry is
embedded in a rich solution space comprising horizonless, naked singularities
and wormhole solutions. Characteristically, the deformed solutions follow the
Schwarzschild solution up outside of the photon sphere while they differ
substantially close to the center of gravity. We then carry out an analytic
analysis of observable signatures accessible to the Event Horizon Telescope,
comprising the size of the black hole shadow as well as the radiation emitted
by infalling matter. On this basis, we argue that it is the brightness within
the shadow region which constrains the phase space of solutions. Our work
constitutes the first step towards bounding the phase space of black hole type
solutions with a clear quantum gravity interpretation based on observational
data.
