Shadow of a renormalization group improved rotating black hole

Abstract

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 χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi $$\\end{document}, with the Lagrangian of the collapsing fluid. The resulting exterior metric for large radii depends on a free parameter ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi $$\\end{document} which captures the quantum gravity effects. The form of the coupling χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi $$\\end{document} and its connection with the quantum parameter ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi $$\\end{document} 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⋆\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a_{\\star }$$\\end{document} and the quantum parameter ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi $$\\end{document}, 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 ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi $$\\end{document}, we confront our results with the recent Event Horizon Telescope (EHT) observations of the shadows of the supermassive BHs M87∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {M87}^*$$\\end{document} and Sgr A∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {A}^*$$\\end{document}. 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.