Scalar Perturbations and Stability of a Loop Quantum Corrected Kruskal Black Hole

TL;DR

This paper studies scalar field perturbations of a loop quantum gravity-inspired black hole, demonstrating its stability, unique oscillation features, and altered wave behavior compared to classical Schwarzschild black holes.

Contribution

It introduces an approximate metric form for the quantum-corrected black hole and analyzes its quasinormal modes and stability properties.

Findings

Black hole is stable against scalar perturbations.

Oscillates at higher frequency with less damping than Schwarzschild.

Exhibits a different power-law tail in the ringdown waveform.

Abstract

We investigate the massless scalar field perturbations of a new loop quantum gravity motivated regular black hole proposed by Ashtekar {\it et al.} in [Phys.Rev.Lett. 121, 241301 (2018), Phys.Rev.D 98, 126003 (2018)]. The spacetime of this black hole is distinguished by its asymptotic properties: in Schwarzschild coordinates one of the metric functions diverges as $r\to \infty$ even though the spacetime is asymptotically flat. We show that despite this unusual asymptotic behavior, the quasinormal mode potential is well defined everywhere when Schwarzschild coordinates are used. We propose a useful approximate form of the metric, which allows us to produce quasinormal mode frequencies and ringdown waveforms to high accuracy with manageable computation times. Our results indicate that this black hole model is stable against massless scalar field perturbations. We show that, compared to the Schwarzschild black hole, this black hole oscillates with higher frequency and less damping. We also observe a qualitative difference in the power-law tail of the ringdown waveform between this black hole model and the Schwarzschild black hole. This suggests the quantum corrections affect the behavior of the waves at large distances from the black hole.