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Description
We obtain quantum parameter-mass induced spontaneous scalarization of quantum Oppenheimer-Snyder (qOS)-black hole in the Einstein-Gauss-Bonnet-scalar (EGBS) theory with the unknown qOS action. It is turned out that two Davies points of heat capacity are identified with two critical onset mass and quantum parameter, showing a strong connection between thermodynamics of bald black hole and spontaneous scalarization. Furthermore, we study onset scalarization of the extremal qOS-black hole in the EGBS theory. To obtain the scalar clouds being seeds to generate two branches of scalarized extremal qOS-black holes, we consider the near-horizon geometry of the Bertotti-Bobinson (BR) spacetime. In this case, it is shown that the appearance of a large scalar cloud at the horizon is a new feature to represent tachyon cloud with negative mass. However, a scalar cloud with standard mass around the BR spacetime blows up at the horizon. Finally, we obtain scalarized extremal qOS-black holes by adopting the entropy function approach.