https://doi.org/10.1140/epjc/s10052-026-15532-3
Regular Article
Charged qOS-extremal black hole and its scalarization by entropy function approach
Center for Quantum Spacetime, Sogang University, 04107, Seoul, Republic of Korea
a
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Received:
21
January
2026
Accepted:
4
March
2026
Published online:
20
March
2026
Abstract
We investigate scalarization of charged quantum Oppenheimer–Snyder extremal (cqOSe)-black hole described by mass M, quantum parameter 
and magnetic charge P in the Einstein–Gauss–Bonnet-scalar theory with a nonlinear electrodynamics term. This scalarization may be equivalent to scalarization of quantum Oppenheimer–Snyder (qOS)-extremal black hole whose action is still unknown when replacing 
by 3M/2. Focusing on the onset of scalarization, we find the single branch of scalarized cqOS extremal (scqOSe)-black holes. To obtain a scalar cloud (seed) for the single branch, however, we have to consider its near-horizon geometry of the Bertotti–Bobinson (BR) spacetime. In this case, two scalar clouds for positive and negative coupling constant 
are found to represent two branches. Applying Sen’s entropy function approach to this theory, we obtain the entropy which is the only physical quantity to describe the scqOSe-black holes. We find that the positive branch is preferred than the negative branch.
© The Author(s) 2026
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