arXiv subjects

Stefan J. Randow

Publications and source records attributed to Stefan J. Randow.

2 recordsLinked to original sources

arXiv2026

Sensitivity of black hole spectral instability to ultraviolet perturbations

Black hole quasinormal modes are known to exhibit spectral instability under ultraviolet perturbations of the effective potential. In the present work, we investigate the sensitivity of the fundamental mode to different types of localized perturbations through a combination of analytic and numerical analyzes. We show that the instability is governed primarily by the effective size of the perturbation rather than by its specific shape. In particular, the instability may persist even in the limit where the width of the perturbation vanishes, provided that the integrated strength of the perturbation is not zero. While a delta-function perturbation destabilizes the fundamental mode through an outward spiral, its interplay with a jump-discontinuity-type perturbation gives rise to competing inward and outward spiral motions. We further show that the stability of the fundamental mode depends sensitively on how the magnitude of the perturbation decreases as it moves away from the compact object, leading to qualitatively distinct outward spirals, inward spirals, and rotational trajectories. Finally, we investigate the motion of the fundamental mode in perturbed Regge-Wheeler potentials containing a jump discontinuity associated with a thin matter shell surrounding the black hole. The resulting behavior qualitatively resembles the spiral structure observed in double-sided Pöschl-Teller potentials, suggesting that the mechanisms identified in analytically tractable models persist in more realistic black hole effective potentials. The present results indicate that the spectral instability of low-lying black hole modes is considerably richer than previously anticipated and may have important implications for black hole spectroscopy in realistic astrophysical environments.

gr-qc↗

arXiv2025

Evolution of black hole echo modes and the causality dilemma

It has been shown that black hole quasinormal modes are subject to spectral instability, typically triggered by metric perturbations. These perturbations, which can introduce a minor bump in the effective potential of the wave equation, give rise to a novel branch of asymptotic quasinormal modes, dubbed the {\it echo modes}, which lie mainly parallel to the real frequency axis. This study explores the evolution of the echo modes and their interplay with the outward spiral motion observed in low-lying quasinormal modes. As the bump in the effective potential moves away from the central black hole, the echo modes collectively shift toward the real axis, with the spacing between successive modes decreasing uniformly. This collective motion occurs simultaneously with the spiral of the low-lying modes until the echo modes eventually take over the fundamental quasinormal mode. In the time domain, such a takeover coincides with a transition point for the temporal waveform, where the distinction between the original black hole's ringdown and the echoes becomes clear. This marks a transition in the characteristics of the waveform from primarily damped oscillations, dominated by the damping rate of the fundamental mode, to echo waves, characterized by periodic echo pulses. We argue that this phenomenon is universal by employing analytical and numerical analyses. We first elucidate our arguments using explicit but simplified toy models, where the effective potential barriers are disjoint. The derivations are then generalized to scenarios where perturbations are introduced on top of a black hole metric with a continuous effective potential. The observational implications, particularly the causality dilemma, are elaborated. We show that the echo modes can be extracted by applying the Fourier transform to ringdown waveforms, which can be important for gravitational wave observations.

gr-qc↗