Effective action and black hole solutions in asymptotically safe quantum gravity

TL;DR

This paper derives the quantum effective action in asymptotically safe quantum gravity, computes graviton scattering couplings, and finds quantum black hole solutions with signatures of quantum effects outside the classical horizon.

Contribution

It reconstructs the quantum effective action from multi-graviton vertices and numerically solves for quantum black hole geometries, revealing new quantum signatures.

Findings

Quantum black hole solutions exhibit signatures outside the classical horizon.

Three distinct types of solutions with different causal structures are identified.

The phase structure of the solution space is explored.

Abstract

We derive the quantum effective action and the respective quantum equations of motion from multi-graviton correlation functions in asymptotically safe quantum gravity. 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. Three different types of solutions with distinct causal structures are identified and the phase structure of the solution space is investigated.