The tachyonic instability of the Kerr black holes is analyzed in the Einstein-scalar theory with the quadratic scalar couplings to two topological terms which are parity-even Gauss-Bonnet and parity-odd Chern-Simons terms. For positive coupling α, we use the (2+1)-dimensional hyperboloidal foliation method to derive the threshold curve which is the boundary between stable and unstable Kerr black holes by considering a spherically symmetric scalar-mode perturbation. In case of negative coupling, a newly bound of a≥0.26 with a the rotation parameter is found for unstable Kerr black holes and its threshold curve is derived.
@article{arxiv.2104.06583,
title = {Rotating scalarized black holes in scalar couplings to two topological terms},
author = {De-Cheng Zou and Yun Soo Myung},
journal= {arXiv preprint arXiv:2104.06583},
year = {2021}
}