Quantum parameter-mass induced scalarization of qOS-black hole in the Einstein-Gauss-Bonnet-scalar theory

Abstract

We obtain quantum parameter ($\alpha$)-mass ($M$) induced spontaneous scalarization of quantum Oppenheimer-Snyder (qOS)-black hole in the Einstein-Gauss-Bonnet-scalar theory with the unknown qOS action. We derive Smarr formula which describes a correct thermodynamics for the bald qOS-black hole. It is turned out that two Davies points of heat capacity are identified with two critical onset mass and quantum parameter for spontaneous scalarization. However, we do not obtain such connections from the Einstein-Gauss-Bonnet-scalar theory with the nonlinear electrodynamics action. Furthermore, the shadow radius analysis of qOS-black hole is performed to distinguish quantum parameter from mass by comparing them with the EHT observation. There is no constraints on the quantum parameter, but new constraints are found for the mass. This work is considered as the first example to show a close connection between thermodynamics of bald black hole and spontaneous scalarization.