Quasibound states of charged Dirac fields around Einstein-Euler-Heisenberg black holes
Abstract
We study quasibound states of a massive charged Dirac field on the Einstein--Euler--Heisenberg (EEH) black hole, the extension of Reissner--Nordström (RN) by the leading weak-field vacuum-polarization term of QED. We derive the background to first order in the Euler--Heisenberg coupling a. We show that it admits a nondegenerate horizon at Q=M and an extremal charge Qext=M[1+a/(40M2)+𝒪(a2)]>M, with horizon data that depend on √a near extremality. From the separated radial equations, we derive an identity that excludes real-frequency quasibound states on any background of this class, so damped branches cannot become unstable. Since the EEH corrections first enter at 𝒪(r−5) in the electrostatic potential, the trapping condition Mμ2−qQωR>0 and the hydrogenic spectrum coincide with RN, and no fine-structure-order splitting arises. Two-sided shooting with a Muller root finder shows that the real frequencies shift only by near-zone amounts that are linear in a and strongly suppressed with angular momentum. The damping rates respond in a branch-dependent way. At Q/M=0.99 the ℓ=0 ground state becomes slightly longer-lived, while the (nr,j,ℓ,λ)=(0,3/2,1,−2) state decays up to 80% faster for a/M2≤1, and near the trapping threshold the damping rate increases by up to 60%. Switching on the metric and potential corrections separately, together with a WKB analysis of the inner barrier, identifies the mechanisms: Coulomb screening always increases leakage, while the metric correction controls the sign and size of the ℓ-dependent effect. Characteristic time-domain evolutions with Richardson-extrapolated matrix-pencil extraction reproduce the frequency-domain shifts.
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BibTeX
@misc{anarboev2026quasibound,
title = {{Quasibound states of charged Dirac fields around Einstein-Euler-Heisenberg black holes}},
author = {Nodirbek Anarboev and Javlonbek Khasanov and Javlon Rayimbaev and Bobomurat Ahmedov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17034},
eprint = {2610.17034},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17034},
}
RIS
TY - UNPB
TI - Quasibound states of charged Dirac fields around Einstein-Euler-Heisenberg black holes
AU - Nodirbek Anarboev
AU - Javlonbek Khasanov
AU - Javlon Rayimbaev
AU - Bobomurat Ahmedov
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.17034
UR - https://arxiv.org/abs/2610.17034
AB - We study quasibound states of a massive charged Dirac field on the Einstein--Euler--Heisenberg (EEH) black hole, the extension of Reissner--Nordström (RN) by the leading weak-field vacuum-polarization term of QED. We derive the background to first order in the Euler--Heisenberg coupling a. We show that it admits a nondegenerate horizon at Q=M and an extremal charge Q_ext=M[1+a/(40M^2)+𝒪(a^2)]>M, with horizon data that depend on √a near extremality. From the separated radial equations, we derive an identity that excludes real-frequency quasibound states on any background of this class, so damped branches cannot become unstable. Since the EEH corrections first enter at 𝒪(r^−5) in the electrostatic potential, the trapping condition Mμ^2−qQω_R>0 and the hydrogenic spectrum coincide with RN, and no fine-structure-order splitting arises. Two-sided shooting with a Muller root finder shows that the real frequencies shift only by near-zone amounts that are linear in a and strongly suppressed with angular momentum. The damping rates respond in a branch-dependent way. At Q/M=0.99 the ℓ=0 ground state becomes slightly longer-lived, while the (n_r,j,ℓ,λ)=(0,3/2,1,−2) state decays up to 80% faster for a/M^2≤1, and near the trapping threshold the damping rate increases by up to 60%. Switching on the metric and potential corrections separately, together with a WKB analysis of the inner barrier, identifies the mechanisms: Coulomb screening always increases leakage, while the metric correction controls the sign and size of the ℓ-dependent effect. Characteristic time-domain evolutions with Richardson-extrapolated matrix-pencil extraction reproduce the frequency-domain shifts.
ER -