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 ₂ that describes the magnitude of the instability of a QNM spectrum. Our analysis reveals that the dependence of ₂ on ϵ is complicated---it may increase, decrease or even be nonmonotonic.