Gravitational Wave Tails and Transient Behaviors of Quantum-Corrected Black Holes

TL;DR

This work investigates how quantum corrections to black-hole spacetimes from effective Loop Quantum Gravity affect gravitational-wave tails and the transition from quasinormal-mode (QNM)–dominated ringing to tail-dominated decay. Using a generalized Teukolsky equation for the leading Weyl scalar $\Psi_4^{(1)}$ on a quantum-corrected background with $F(r)=1-\frac{2M}{r}+27\left(\frac{\alpha M}{2r}\right)^4$, and solving in horizon-penetrating hyperboloidal coordinates via a spectral method, the authors find that tail amplitudes and intermediate decay behavior depend on the quantum parameter $\alpha$. While the late-time tails retain GR-like power-law decay, their amplitudes and the timing of the QNM-to-tail transition are sensitive to $\alpha$ and initial data, with non-compact initial data showing larger effects (up to an order of magnitude) and occasional nonmonotonic behavior (including rare cases where the tail amplitude increases with $\alpha$). Given that $\alpha$ scales as $\alpha\sim\sqrt{l_p/r_{BH}}$, these quantum-tail effects are unlikely to be observable for astrophysical black holes, but the results highlight that tail features carry dynamical information about BHs and should be treated cautiously in precise gravitational-wave waveform modeling and in broader tests of general relativity.

Abstract

Gravitational wave astronomy plays a pivotal role in testing the dynamics of gravity in strong-field regimes and probing the nature of black holes. Motivated by recent studies on late-time tails in gravitational waves, we examine the gravitational wave tails of black holes incorporating quantum corrections within the framework of effective Loop Quantum Gravity. Our findings indicate that both the amplitudes and the intermediate behavior of these tails are influenced by quantum corrections. We demonstrate that the amplitude and transient characteristics of the tail are sensitive to the specific details of the black hole's dynamics.

Figures (2)

• Figure 1: Late-time tails for compact Gaussian initial data. Results are shown for varying quantum modification parameter $\alpha$, the center of the Gaussian wave packet $R_0$, and width $w_0$. In the late-time tail regime, the power-law decay is consistent with that in the classical GR case. However, the amplitude of the tail and the transition from the QNM-dominated phase to the tail-dominated phase are sensitive to $\alpha$.
• Figure 2: Late-time tails for non-compact Gaussian initial data. Results are shown for varying quantum modification parameter $\alpha$, the center of the Gaussian wave packet $R_0$, and width $w_0$. Compared to compact initial data, non-compact initial data produces a relatively larger impact on the amplitude under the same parameter settings, with differences reaching up to an order of magnitude.