Black holes in an asymptotically safe gravity theory with higher derivatives

Abstract: We present a class of spherically symmetric vacuum solutions to an asymptotically safe theory of gravity containing high-derivative terms. We find quantum corrected Schwarzschild-(anti)-de Sitter solutions with running gravitational coupling parameters. The evolution of the couplings is determined by their corresponding renormalization group flow equations. These black holes exhibit properties of a classical Schwarzschild solution at large length scales. At the center, the metric factor remains smooth but the curvature singularity, while softened by the quantum corrections, persists. The solutions have an outer event horizon and an inner Cauchy horizon which equate when the physical mass decreases to a critical value. Super-extremal solutions with masses below the critical value correspond to naked singularities. The Hawking temperature of the black hole vanishes when the physical mass reaches the critical value. Hence, the black holes in the asymptotically safe gravitational theory never completely evaporate. For appropriate values of the parameters such stable black hole remnants make excellent dark matter candidates.