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

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 $\epsilon$ 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 $\epsilon$. As for the time domain, the mismatch function is introduced and found to scale as ${\epsilon }^2$, which demonstrates that the waveform is stable as $\epsilon$ 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 $\epsilon$ is complicated -- it may increase, decrease or even be nonmonotonic.

20 pages, 9 figures

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