The impact of plunging matter on black-hole waveform

TL;DR

The paper investigates how dynamical environmental matter around a black hole modifies ringdown gravitational waves. It employs a phenomenological axial perturbation framework in Schwarzschild spacetime, adding a Gaussian bump to the Regge-Wheeler potential and studying both stationary and time-dependent cases, including geodesic-like and constant-velocity motions. Key findings show that static bumps can create cavity structures producing echoes, whose presence and properties depend on the bump location; moving bumps can either suppress or generate echoes and induce frequency shifts and complex late-time tails, depending on motion type and initial conditions. The results offer potential observational signatures to probe near-horizon environments and dynamical hair around black holes, informing interpretation of future gravitational wave detections and motivating more realistic, nonlinear models and backreaction studies. The analysis provides a theoretical foundation for connecting environmental matter dynamics to measurable deviations in ringdown signals.

Abstract

In this work, we introduce a novel framework to investigate ringdown gravitational waveforms in the presence of dynamical matter fields outside the horizon of a black hole. We systematically analyze two distinct scenarios of dynamical matter fields: motion along geodesics and uniform motion with constant velocity. Our results reveal rich phenomenology in the ringdown gravitational wave signals, including the suppression or enhancement of echoes, frequency shifts in the decay oscillations, and intricate modulations of the power-law tails. Notably, we demonstrate that subluminal moving potentials can produce irregular echo patterns and shift the dominant frequencies, offering potential new observational signatures beyond the already-known ringdown analyses. This study provides a new perspective for probing dynamic environments around black holes and offers a theoretical foundation for interpreting possible deviations in future gravitational wave detections.

Figures (5)

• Figure 1: In the left column, we present the relative positions of the Gaussian bump and the Regge-Wheeler potential corresponding to different values of $a$. Meanwhile, we present the time-domain ringdown waveforms in the middle column and the corresponding logarithmic plots in the right column for various values of the parameter $a$.
• Figure 2: The figure shows the velocity distributions referring to radial and tortoise coordinates. The black curves correspond to a free fall from infinity, while the blue, red, and green curves represent finite initial positions $a_0 = 20, 3, -20$, respectively.
• Figure 3: Waveforms of axial gravitational field perturbation with an additional bump moving along the geodesics. The blue and green curves correspond to the motion with and without the initial velocity, respectively. The black curve denotes the vacuum reference case.
• Figure 4: Waveforms of axial gravitational field perturbations with an additional bump moving at constant velocity. The blue, green, and red curves correspond to velocities $v=0.5$, $0.8$, and $1$, respectively. The black curve denotes the vacuum reference case.
• Figure 5: Profiles of the matter functions $\rho(r)$, $p_r(r)$, and $p_t(r)$ as functions of the radial coordinate. The red, green, blue, and black curves correspond to bump positions $a = 60, 20, 3, -20$, respectively. A severe divergence occurs for the value of $a = -60$ at $r \rightarrow 1$, this situation is consequently omitted. Here $\chi=0.5$ and $2M = 1$ are set.