Black Holes In Asymptotic Safety With Higher Derivatives: Accretion And Stability Analysis

We review steady spherically symmetric accretion onto a renormalization group improved Schwarzschild space-time, which is a solution to an asymptotically safe theory (AS) containing high-derivative terms. We use a Hamiltonian dynamical system approach for the analysis of the accretion of four types of isothermal test fluids: ultra-stiff fluid, ultra-relativistic fluid, radiation fluid, and sub-relativistic fluid. An important outcome of our study is that, contrary to the claim in a recent work, there are physical solutions for the accretion of an ultra-relativistic fluid in AS, which include subsonic, supersonic, and transonic regimes. Furthermore, we study quantum corrections to the known stability of the accretion in general relativity (GR). To this end, we use a perturbative procedure based on the continuity equation with the mass accretion rate being the perturbed quantity. Two classes of perturbations are studied: standing and traveling waves. We find that quantum gravity effects either enhance or diminish the stability of the accretion depending on the type of test fluid and the radial distance to the central object.