Parity violating spectral dynamics of black holes in dynamical Chern-Simons gravity

Abstract

We study how environmentally driven spectral instabilities of quasinormal modes respond to parity violating gravito-scalar coupling in black holes. Focusing on dynamical Chern-Simons gravity as a paradigm for parity violation, we perturb the Schwarzschild background with a localized potential bump. Our analysis reveals three distinctive phenomena absent in general relativity: 1) branch reconnections in the complex frequency plane, 2) a counterintuitive mode stabilization that delays overtaking transitions, and 3) scalar mode dominance emerging at intermediate coupling strengths. These frequency domain features show how comparatively weak static sector differences manifest as distinct dynamical signatures, thereby linking parity violating black hole perturbations with non-Hermitian spectral physics. Our results provide a frequency domain characterization of parity violating coupling and motivate future targeted ringdown studies of modified gravity.