Shadow of a Renormalization Group Improved Regular Rotating Black Hole

We present a study on quantum gravity effects on the shadow of a regular rotating black hole (BH) obtained in the setting of the asymptotic safety (AS) gravity. We show that the rotating metric, which results from a static regular one recently presented in the literature, remains regular after being constructed using the generalized Newman-Janis (NJ) 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 (UV) non-gaussian fixed point of the AS theory. 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 shadow features of rotating BHs. In order to obtain constraints on the parameter xi, we confront our results with the recent 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 regular rotating BH.