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arXiv · 2609.02380

The Analytical Solutions of Dyonic Black Holes in Einstein-Euler-Heisenberg Theory

Haoyuan Luo·Nan Cao·Xiao Yan Chew·Kok-Geng Lim·Chao Chen·Dong-han Yeom
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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 $2b\rightarrow a$.

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Haoyuan Luo, Nan Cao, Xiao Yan Chew, Kok-Geng Lim, Chao Chen, Dong-han Yeom. 2026-09-02. The Analytical Solutions of Dyonic Black Holes in Einstein-Euler-Heisenberg Theory. https://arxiv.org/abs/2609.02380

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