https://doi.org/10.1140/epjc/s10052-022-10910-z
Regular Article - Theoretical Physics
On the late-time tails of massive perturbations in spherically symmetric black holes
1
Center for Gravitation and Cosmology, School of Physical Science and Technology, Yangzhou University, 225009, Yangzhou, Jiangsu, China
2
Escola de Engenharia de Lorena, Universidade de São Paulo, 12602-810, Lorena, SP, Brazil
3
Faculdade de Engenharia de Guaratinguetá, Universidade Estadual Paulista, 12516-410, Guaratinguetá, SP, Brazil
4
Hubei Subsurface Multi-scale Imaging Key Laboratory, Institute of Geophysics and Geomatics, China University of Geosciences, 430074, Wuhan, Hubei, China
5
MOE Key Laboratory of Fundamental Physical Quantities Measurement, Hubei Key Laboratory of Gravitation and Quantum Physics, PGMF, and School of Physics, Huazhong University of Science and Technology, 430074, Wuhan, Hubei, China
6
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, 200240, Shanghai, China
Received:
21
June
2022
Accepted:
11
October
2022
Published online:
19
October
2022
It was first pointed out by Koyama and Tomimatsu that, under reasonable assumptions, the asymptotic late-time tails of massive scalar perturbations in the far zone of spherically symmetric black hole spacetimes decay universally as 
. The late-time tail is furnished by the contribution from the branch cut of the frequency-domain Green’s function, which is constructed in terms of two appropriate solutions of the corresponding homogeneous equation. The present study focuses on some particular forms of the in-going wave that were not explicitly considered in the original derivations but nonetheless have been taken into account in the literature by other authors. In this regard, we reassess the authors’ arguments and provide a detailed complimentary analysis that covers a few specific aspects. For some particular cases, the tail is found to possess the form 
. We also discuss the possible implications of the present findings.
© The Author(s) 2022
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