qOS-induced scalarization of black holes in extended scalar-tensor theories

In the extended scalar-tensor-Gauss-Bonnet (ESTGB) theory, spontaneous scalarization has been extensively studied in various types of black holes. Research indicates that in the GB⁻ regime, where the coupling constant $\lambda <0$, spontaneous scalarization typically occurs in rotating black holes, a phenomenon known as spin-induced scalarization. Recently, by studying the quantum Oppenheimer-Snyder (qOS) gravitational collapse model, a qOS-corrected Schwarzschild black hole has been proposed. By numerically calculating the time evolution of scalar perturbations, we have, for the first time, obtained the spontaneous scalarization region for the qOS-corrected Schwarzschild black hole in the ESTGB theory. Surprisingly, we found that GB⁻ scalarization can also occur in this spherically symmetric black hole. We refer to this phenomenon as qOS-induced spontaneous scalarization. Our results show that the range of the quantum parameter $\alpha /M^2$ which allows GB⁻ scalarization increases as the coupling constant $-\lambda /M^2$ grows. When $-\lambda /M^2$ is small, GB⁻ scalarization can only occur near the extremal black hole limit. As $-\lambda /M^2$ approaches infinity, the lower boundary of $\alpha /M^2$ for GB⁻ scalarization converges to a critical value ${(\alpha /M^2)}_{\text{crit}}\simeq 1.2835$, which has been obtained analytically. Since the quantum parameter is typically small, our results suggest that spontaneous scalarization primarily affects microscopic black holes, offering valuable insights into the study of the early universe, primordial black holes and quantum black holes.