Work

Waveform stability for the piecewise step approximation of Regge–Wheeler potential

Year: 2026

Type: article

Abstract: By interpreting the difference between the original Regge–Wheeler potential and its piecewise step approximation as perturbative effects induced by the external environment of the black hole, we investigate the stability of Schwarzschild black hole time-domain waveforms. In this work, we employ the Green’s function method under the assumption of an observer at spatial infinity to obtain the waveform. For two cases in which the initial Gauss bump near the event horizon or at spatial infinity, we derive analytic expressions for the corresponding waveforms. Our results demonstrate that the waveform is indeed insensitive to tiny modifications of the effective potential, thereby confirming its stability. More importantly, we find that broader initial bumps imprint the influence of small environmental modifications more clearly on the waveform, which may provide theoretical guidance for probing the exterior environment of black holes.

Source: The European Physical Journal C

DOI: 10.1140/epjc/s10052-026-15616-0

Authors: Liang-Bi Wu, Libo Xie, Yu-Sen Zhou, Zong-Kuan Guo, Rong-Gen Cai

Institutions: University of Chinese Academy of Sciences, Chinese Academy of Sciences, University of Science and Technology of China, Ningbo University

Language: English

Topic: Pulsars and Gravitational Waves Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4414789951

FWCI: 9.905

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Cited by: 3

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