Analytical computation of quasinormal modes of slowly rotating black holes in dynamical Chern-Simons gravity

Using gravitational wave observations to search for deviations from general relativity in the strong-gravity regime has become an important research direction. Chern Simons (CS) gravity is one of most frequently studied parity-violating models strong gravity. It known that Kerr black-hole not a solution CS At same time, only rotating available literature dynamical (dCS) slow-rotating case accurately quadratic order spin. In this work, (accurate first spin), we derive linear perturbation equations governing metric and dCS field accurate spin coupling parameter ($\alpha$) obtain quasi-normal mode (QNM) frequencies. After confirming recent results Wagle et al. (2021), find additional contribution eigenfrequency correction at leading perturbative $\alpha^2$. Unlike al., also corrections frequencies polar sector. We compute these extra by evaluating expectation values potential on unperturbed QNM wavefunctions along contour deformed into complex-$r$ plane. For $\alpha=0.1 M^2$, ratio imaginary parts GR frequency (in sector) be $0.263$ implying significant change. $(2,2)-$mode, make part fundamental less negative, thereby decreasing decay rate. Our results, with future observations, can used test further constrain parameters. [abridged]