The Analytical Solutions of Dyonic Black Holes in Einstein-Euler-Heisenberg Theory
Abstract
Recently, we constructed analytical purely electric and purely magnetic black-hole solutions in Einstein--Euler--Heisenberg theory, while the corresponding dyonic solutions were obtained numerically \cite{Luo:2026srx}. Motivated by the recent analytical construction of a dyonic black hole at the special coupling locus b=a/2 \cite{Ahmed:2026ufj}, we revisit the general dyonic sector. We show that exact analytical dyonic black-hole solutions can be constructed for nonlinear couplings satisfying 2b>a, without imposing the restriction b=a/2. The mass function is expressed in closed form in terms of the Lauricella hypergeometric function. In particular, our construction yields an exact dyonic solution for the Euler--Heisenberg coupling b=7a/4. The solution of Ref.~\cite{Ahmed:2026ufj} is recovered in the limiting case 2b→ a.
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BibTeX
@misc{luo2026analytical,
title = {{The Analytical Solutions of Dyonic Black Holes in Einstein-Euler-Heisenberg Theory}},
author = {Haoyuan Luo and Nan Cao and Xiao Yan Chew and Kok-Geng Lim and Chao Chen and Dong-han Yeom},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02380},
eprint = {2609.02380},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02380},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - The Analytical Solutions of Dyonic Black Holes in Einstein-Euler-Heisenberg Theory
AU - Haoyuan Luo
AU - Nan Cao
AU - Xiao Yan Chew
AU - Kok-Geng Lim
AU - Chao Chen
AU - Dong-han Yeom
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02380
UR - https://arxiv.org/abs/2609.02380
AB - Recently, we constructed analytical purely electric and purely magnetic black-hole solutions in Einstein--Euler--Heisenberg theory, while the corresponding dyonic solutions were obtained numerically \cite{Luo:2026srx}. Motivated by the recent analytical construction of a dyonic black hole at the special coupling locus b=a/2 \cite{Ahmed:2026ufj}, we revisit the general dyonic sector. We show that exact analytical dyonic black-hole solutions can be constructed for nonlinear couplings satisfying 2b>a, without imposing the restriction b=a/2. The mass function is expressed in closed form in terms of the Lauricella hypergeometric function. In particular, our construction yields an exact dyonic solution for the Euler--Heisenberg coupling b=7a/4. The solution of Ref.~\cite{Ahmed:2026ufj} is recovered in the limiting case 2b→ a.
ER -