https://doi.org/10.1140/epjc/s10052-025-15232-4
Regular Article - Theoretical Physics
New scalarization of the Einstein–Euler–Heisenberg black hole
1
College of Science, Hunan Institute of Technology, 421002, Hengyang, China
2
College of Physics and Communication Electronics, Jiangxi Normal University, 330022, Nanchang, China
3
Center for Quantum Spacetime, Sogang University, 04107, Seoul, Republic of Korea
a
This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
10
October
2025
Accepted:
14
December
2025
Published online:
24
December
2025
Abstract
The spontaneous scalarization of the Einstein–Euler–Heisenberg (EEH) black hole is performed in the EEH-scalar theory by introducing an exponential scalar coupling (with 
coupling constant) to the Maxwell term. Here, the EEH black hole as a blad black hole is described by mass M and magnetic charge q with an action parameter 
. A choice of 
guarantees a single horizon with unrestricted magnetic charge q. The onset scalarization of this black hole appears for a positive coupling with an unlimited magnetic charge q. However, there exists a difference between 
and 
onset scalarizations. We notify the presence of infinite branches labeled by the number of 
of scalarized charged black holes by taking into account the scalar seeds around the EEH black hole. We find that the 
fundamental branch of all scalarized black holes is stable against the radial perturbations, while the 
excited branch is unstable.
© The Author(s) 2025
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3.
