Quantum gravitational corrections to the Schwarzschild spacetime and quasinormal frequencies

Abstract: Quantum gravitational corrections to the entropy of the Schwarzschild black hole, derived using the Wald entropy formula within an effective field theory framework, were presented in [X. Calmet, F. Kuipers Phys.Rev.D 104 (2021) 6, 066012]. These corrections result in a Schwarzschild spacetime that is deformed by the quantum correction. However, it is observed that the proposed quantum-corrected metric describes not a black hole, but a wormhole. Nevertheless, further expansion of the metric function in terms of the quantum correction parameter yields a well-defined black hole metric whose geometry closely resembles that of a wormhole. We also explore methods for distinguishing between these quantum-corrected spacetimes based on the quasinormal frequencies they emit. We show that while the fundamental mode deviates from the Schwarzschild limit only mildly, the first few overtones deviate at a strongly increasing rate, creating a characteristic ``sound'' of the event horizon.