Black Holes in Asymptotically Safe Gravity

In this chapter, we review the state-of-the-art of black holes in asymptotically safe gravity. After a brief recap of the asymptotic safety program, we shall summarize derivations and features of the main asymptotic safety-inspired models that have been constructed in the past by the so-called renormalization group improvement. Specifically, we will discuss static configurations, both in spherically and axially symmetric settings, the role played by the cosmological constant, and the impact of the collapse dynamics in determining black hole configurations realized in nature. In particular, we will review how quantum gravity could modify the Buchdahl limit and the corresponding conditions to form ultra-compact objects and Planckian black holes. We will then proceed by describing the most recent developments, particularly those aiming at making model building in asymptotic safety more rigorous and free from ambiguities. These include self-consistent and coordinate-independent versions of the renormalization group improvement and next steps to fill the gap between model building and renormalization group computations in asymptotic safety. Finally, we will focus on a selection of results that have been obtained from first-principle calculations or arguments, within and beyond asymptotic safety. Concretely, we will review the state-of-the-art in determining black hole entropy in asymptotic safety from a microstate counting and progress in deriving the quantum-corrected Newtonian potential. We will discuss how in quantum gravity theories linked to a gravitational path integral singularity resolution could be achieved by a dynamical suppression of singular configurations and how this is related to the form of the bare action. Finally, we will show that – independent of the specific ultraviolet completion of gravity – asymptotic modifications to Schwarzschild black holes are strongly constrained by the principle of least action at large-distance scales.