  We study the formation and perturbation of black holes by null fluxes of
neutral matter in a quadratic extension of General Relativity formulated a la
Palatini. Working in a spherically symmetric space-time, we obtain an exact
analytical solution for the metric that extends the usual Vaidya-type solution
to this type of theories. We find that the resulting space-time is formally
that of a Reissner-Nordstrom black hole but with an effective charge term
carrying the wrong sign in front of it. This effective charge is directly
related to the luminosity function of the radiation stream. When the ingoing
flux vanishes, the charge term disappears and the space-time relaxes to that of
a Schwarzschild black hole. We provide two examples that illustrate the
formation of a black hole from Minkowski space and the perturbation by a finite
pulse of radiation of an existing Schwarzschild black hole.
