Scalarized Einstein-Euler-Heisenberg black holes at the approach to extremality
Abstract
We investigate extremal black holes with scalar hair in the generic Einstein-Euler-Heisenberg (EEH)-scalar theory with two scalar couplings to the Maxwell term. One is an exponential coupling with coupling constant α and the other is its polynomial coupling. We first construct scalarized black holes on the cold (C)-horizon of EEH black holes described by mass M and magnetic charge P both at the linear level, through the existence curves αn(q) with q=P/M, and as fully backreaction solutions. As extremality (q=qe) is approached, all existence curves accumulate, following αn−αc∼ 1/ln2(qe−q), at the critical branch αc fixed by the Breitenlohner-Freedman bound for the near-horizon (AdS2× S2) throat. We obtain scalarized extremal black hole (SEBH) with constant secondary hair and it is recovered exactly from the entropy function approach working on the near-horizon throat. Its entropy is an attractor invariant, being independent of the asymptotic modulus, so the scalar hair remains secondary. Exploiting this constant scalar, we seek further SEBHs with scalar hair keeping its charge Qs for the zero asymptotic scalar (ϕ∞=0). In the (q,α) plane, we observe that these extremal solutions occupy q≥ qe. Hence, the existence curves αn(q) existing for q≤ qe and the extremal branches bound the scalarized domain from opposite sides and they meet only at q=qe.
Related
- The Analytical Solutions of Dyonic Black Holes in Einstein-Euler-Heisenberg Theory
- Horizon Structure and Geodesic Properties of Simpson-Visser Black Holes in Einstein-Euler-Heisenberg Theory
- Charge-dependent scalarization of Einstein- Euler-Heisenberg black holes
- Geometric Capture and Optical Critical Curves of Purely Electric, Magnetic and Dyonic Black Holes in Einstein-Euler-Heisenberg Theory
- Tidal Response Beyond the Background Geometry in Einstein-Euler-Heisenberg Black Holes
BibTeX
@misc{guo2026scalarized,
title = {{Scalarized Einstein-Euler-Heisenberg black holes at the approach to extremality}},
author = {Hong Guo and Xiao Yan Chew and Yun Soo Myung},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08128},
eprint = {2609.08128},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08128},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Scalarized Einstein-Euler-Heisenberg black holes at the approach to extremality
AU - Hong Guo
AU - Xiao Yan Chew
AU - Yun Soo Myung
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08128
UR - https://arxiv.org/abs/2609.08128
AB - We investigate extremal black holes with scalar hair in the generic Einstein-Euler-Heisenberg (EEH)-scalar theory with two scalar couplings to the Maxwell term. One is an exponential coupling with coupling constant α and the other is its polynomial coupling. We first construct scalarized black holes on the cold (C)-horizon of EEH black holes described by mass M and magnetic charge P both at the linear level, through the existence curves α_n(q) with q=P/M, and as fully backreaction solutions. As extremality (q=q_e) is approached, all existence curves accumulate, following α_n−α_c∼ 1/ln^2(q_e−q), at the critical branch α_c fixed by the Breitenlohner-Freedman bound for the near-horizon (AdS_2× S^2) throat. We obtain scalarized extremal black hole (SEBH) with constant secondary hair and it is recovered exactly from the entropy function approach working on the near-horizon throat. Its entropy is an attractor invariant, being independent of the asymptotic modulus, so the scalar hair remains secondary. Exploiting this constant scalar, we seek further SEBHs with scalar hair keeping its charge Q_s for the zero asymptotic scalar (ϕ_∞=0). In the (q,α) plane, we observe that these extremal solutions occupy q≥ q_e. Hence, the existence curves α_n(q) existing for q≤ q_e and the extremal branches bound the scalarized domain from opposite sides and they meet only at q=q_e.
ER -