  We present a study on quantum gravity effects on the shadow of a rotating
black hole (BH) obtained in the setting of the asymptotically safe gravity. The
rotating metric, which results from a static regular one recently presented in
the literature, is generated by using the generalized Newman-Janis algorithm.
The novelty of the static regular metric lies in the fact that it is the
outcome of an effective Lagrangian which describes dust whose spherically
symmetric collapse is non-singular as a consequence of the antiscreening
character of gravity at small distances. The effective Lagrangian includes a
multiplicative coupling, denoted as chi, with the Lagrangian of the collapsing
fluid. The resulting exterior metric for large radii depends on a free
parameter xi which captures the quantum gravity effects. The form of the
coupling chi and its connection with the quantum parameter xi are determined by
the running of the Newton coupling G(k) along a renormalization group
trajectory that stops at the ultraviolet non-gaussian fixed point of the
asymptotic safety theory for quantum gravity. Varying both the spin parameter
a/M and the quantum parameter xi, we explore the quantum gravity effects on
several astronomical observables used to describe the morphology of the shadow
cast by rotating BHs. In order to obtain constraints on the parameter xi, we
confront our results with the recent Event Horizon Telescope (EHT) observations
of the shadows of the supermassive BHs M87 and Sgr A. We find that the ranges
of variation of all the studied shadow observables fall entirely within the
ranges determined by the EHT collaboration. We then conclude that the current
astronomical data do not rule out the renormalization group improved rotating
BH.
