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arXiv · 2508.13894

Pseudospectrum and time-domain analysis of the EFT corrected black holes

Li-Ming Cao·Ming-Fei Ji·Liang-Bi Wu·Yu-Sen Zhou
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Abstract

We study the linear perturbations of a spherically symmetric black hole corrected by dimension-6 terms in the effective field theory (EFT) of gravity. The solution is asymptotically flat and characterized by two parameters -- a mass parameter $M$ and a dimensionless parameter $\varepsilon$ related to the EFT length scale $l$, and the perturbation equation incorporates a velocity factor which is not constant. The quasinormal modes (QNMs) and time-domain waveforms are studied within the hyperboloidal framework. This approach reproduces the breakdown of the isospectrality and reveals that higher overtones are more sensitive to $\varepsilon$. As for the time domain, the mismatch function is introduced and found to scale as $\varepsilon^2$, which demonstrates that the waveform is stable as $\varepsilon$ varies. Finally, a velocity-dependent energy norm is employed to compute the pseudospectrum and characterize the migration of the QNM spectrum. We further define a quantity $\epsilon_c$ that describes the magnitude of the instability of a QNM spectrum. Our analysis reveals that the dependence of $\epsilon_c$ on $\varepsilon$ is complicated -- it may increase, decrease or even be nonmonotonic.

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Li-Ming Cao, Ming-Fei Ji, Liang-Bi Wu, Yu-Sen Zhou. 2025-08-19. Pseudospectrum and time-domain analysis of the EFT corrected black holes. https://doi.org/10.1103/jc1v-g6hc

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