Improved Reissner-Nordstr\"om-(A)dS Black Hole in Asymptotic Safety

Abstract

This paper studies the quantum modifications of the Reissner-Nordstr\"{o}m-(A)dS black hole within Quantum Einstein Gravity, coupled to an electromagnetic sector. Quantum effects are introduced on the level of the improvements of the classical solution, where the originally constant couplings ($G_0$, $\Lambda_0$, and $\alpha_0$) are promoted to scale dependent quantities ($G_k$, $\Lambda_k$, and $\alpha_k$). Those running couplings are calculated in the functional renormalization group approach. A crucial point of this, so called "improving solutions" procedure is the scale setting where the arbitrary scale $k$ acquires physical meaning due to a relation to the coordinate scale $r$. It is proposed to use such scale settings which are stable after iterative improvements. Using this method one finds that for those improved solutions, there is no stable remnant and due to the appearance of a new internal horizon, there is also no necessity to impose a minimal black hole mass for charged black holes, in order to avoid the the cosmic censorship hypothesis.