Quantum Gravity Corrections to the Scalar Quasi-Normal Modes in Near-Extremal Reissener-Nordstr\"{o}m Black Holes

TL;DR

This paper studies how quantum gravity effects modify scalar quasi-normal modes in near-extremal Reissner-Nordström black holes, revealing significant shifts in frequencies that could impact black hole observations.

Contribution

It introduces a quantum-corrected framework for scalar QNMs in near-extremal black holes using JT gravity and path integral methods, extending results beyond classical approximations.

Findings

Quantum corrections cause notable shifts in QNM frequencies' real parts.

Imaginary parts of QNM frequencies are relatively unaffected by quantum effects.

Results suggest potential observable signatures of quantum gravity in black hole spectra.

Abstract

We investigate quantum corrections to scalar quasi-normal modes (QNMs) in the near-extremal Reissner-Nordstr\"om black hole background with quantum correction in the near-horizon AdS$_2\times \mathrm{S}^2$ region. By performing a dimensional reduction, we obtain an effective Jackiw-Teitelboim (JT) gravity theory, whose quantum fluctuations are captured by the Schwarzian action. Using path integral techniques, we derive the quantum-corrected scalar field equation, which modifies the effective potential governing the QNMs. These corrections are extended from the near-horizon region to the full spacetime via a matching procedure. We compute the corrected QNMs using both the third-order WKB method and the Prony method and find consistent results. Our analysis reveals that quantum corrections can lead to substantial shifts in the real parts of QNM frequencies, particularly for small-mass or near-extremal black holes, while the imaginary parts remain relatively stable. This suggests that quantum gravity effects may leave observable imprints on black hole perturbation spectra, which could be potentially relevant for primordial or microscopic black holes.