Quantum Gravity Corrections to the Scalar Quasi-Normal Modes in Near-Extremal Reissener-Nordström Black Holes

TL;DR

This work addresses quantum corrections to scalar QNMs in near-extremal RN black holes by exploiting the $AdS_2$ JT gravity description of the near-horizon region and its Schwarzian boundary modes. A quantum-corrected scalar equation is derived by integrating over the Schwarzian sector and then matched to the full spacetime to obtain a corrected effective potential. The QNM spectrum is computed with a third-order WKB method and the Prony method, revealing sizable shifts in the real parts of frequencies, especially for small mass or near-extremal black holes, while imaginary parts remain relatively stable. The results suggest observable imprints of IR quantum gravity in black-hole perturbations, with potential relevance for primordial or microscopic black holes and for IR completions of gravity.

Abstract

We investigate quantum corrections to scalar quasi-normal modes (QNMs) in the near-extremal Reissner-Nordström 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.

Figures (8)

• Figure 1: 3-point vertices of the Schwarzian action
• Figure 2: 4-point vertices of the Schwarzian action
• Figure 3: The effective potential. The blue line and the red line represent the classical and the quantum corrected effective potentials for the scalar field, respectively, in the RN black hole background.
• Figure 4: The time evolution of the scalar field in the RN black hole background without quantum correction
• Figure 5: The time evolution of the scalar field in the RN black hole background with quantum correction