Jan Tränkle: Effective action and black hole solutions in asymptotically safe quantum gravity

Exploring quantum corrections to black hole geometries might offer a unique opportunity for observationally testing the asymptotic safety scenario in quantum gravity. With this goal in mind, I will present our recent work on reconstructing the gravitational effective action and computing black hole solutions to the effective field equations. We derive the quantum effective action and the respective quantum equations of motion from asymptotically safe graviton correlation functions. The fully momentum-dependent couplings of three- and four-graviton scatterings are computed within the functional renormalisation group approach and the effective action is reconstructed from these vertices. The resulting quantum equations of motion are solved numerically for quantum black hole geometries. Importantly, the black hole solutions show signatures of quantum gravity outside the classical horizon, which manifest in the behaviour of the temporal and radial components of the metric. We identify three different types of solutions with distinct causal structures and discuss the phase structure of the solution space.

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