Quasi-bound states and late-time evolution of a massive fermion around a Reissner-Nordström black hole
Abstract
A massive fermion around a charged black hole provides a gravitational analogue of atomic bound states and their relaxation. In this work, we study this system by formulating the radial equation as a coupled matrix system and constructing the Green's function with ingoing boundary conditions at the horizon and decaying boundary conditions at infinity. In the weak-coupling scenario |qQ|∼ mM<1, a matrix matching scheme gives an improved analytic expression of quasi-bound-state spectrum, including fine-structure corrections and more accurate decay widths. The extremal Reissner-Nordström case (|Q|=M) is treated separately and shown to be the smooth limiting result of the non-extremal spectrum. We further analyze the branch-cut contribution to the time-domain Green's function in the late-time limit. We confirm an oscillatory power-law behavior in intermediate late-time regime 1/m < t < 1/m3M2. In the far late-time regime t>1/m3M2, the activation of the quasi-bound states produces an t−5/6exp(−ηt1/3) suppression with a chirping phase before the asymptotic t−5/6 tail previously found in the limit t→∞. Direct time-domain simulations support this distinction and show how the quasi-bound contribution coexists with the familiar power-law component.
Versions
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BibTeX
@misc{chen2026quasibound,
title = {{Quasi-bound states and late-time evolution of a massive fermion around a Reissner-Nordström black hole}},
author = {Guang-Shang Chen and Cheng-Bo Yang and Shou-Shan Bao and Yue-Liang Wu and Hong Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.08258},
eprint = {2607.08258},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.08258},
}
RIS
TY - UNPB
TI - Quasi-bound states and late-time evolution of a massive fermion around a Reissner-Nordström black hole
AU - Guang-Shang Chen
AU - Cheng-Bo Yang
AU - Shou-Shan Bao
AU - Yue-Liang Wu
AU - Hong Zhang
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2607.08258
UR - https://arxiv.org/abs/2607.08258
AB - A massive fermion around a charged black hole provides a gravitational analogue of atomic bound states and their relaxation. In this work, we study this system by formulating the radial equation as a coupled matrix system and constructing the Green's function with ingoing boundary conditions at the horizon and decaying boundary conditions at infinity. In the weak-coupling scenario |qQ|∼ mM<1, a matrix matching scheme gives an improved analytic expression of quasi-bound-state spectrum, including fine-structure corrections and more accurate decay widths. The extremal Reissner-Nordström case (|Q|=M) is treated separately and shown to be the smooth limiting result of the non-extremal spectrum. We further analyze the branch-cut contribution to the time-domain Green's function in the late-time limit. We confirm an oscillatory power-law behavior in intermediate late-time regime 1/m < t < 1/m^3M^2. In the far late-time regime t>1/m^3M^2, the activation of the quasi-bound states produces an t^−5/6exp(−ηt^1/3) suppression with a chirping phase before the asymptotic t^−5/6 tail previously found in the limit t→∞. Direct time-domain simulations support this distinction and show how the quasi-bound contribution coexists with the familiar power-law component.
ER -