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.