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

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 $ϵ$ 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 $ϵ$. As for the time domain, the mismatch function is introduced and found to scale as ${ϵ}^{2}$, which demonstrates that the waveform is stable as $ϵ$ 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 ${\ensuremath{\epsilon}}_{c}$ that describes the magnitude of the instability of a QNM spectrum. Our analysis reveals that the dependence of ${\ensuremath{\epsilon}}_{c}$ on $ϵ$ is complicated---it may increase, decrease or even be nonmonotonic.