Parity breaking reshapes black hole spectral dynamics

Abstract

We propose a dynamical amplification mechanism for detecting symmetry breaking in black holes through environmentally driven spectral instabilities of quasinormal modes. 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) topological reconnections of mode branches, 2) counterintuitive mode stabilization that delays overtaking transitions, and 3) scalar mode dominance emerging at intermediate coupling strengths. These dynamical features amplify weak static splittings into observable signatures, establishing a connection between gravitational symmetry breaking and non-Hermitian spectral physics. Our framework provides new pathways for testing modified gravity theories through gravitational wave observations.

Figures (4)

• Figure 1: QNM migration trajectories in the complex frequency plane for different symmetry-breaking strengths $\beta$.
• Figure 2: Scalar mode migration trajectories in the complex frequency plane for $\beta = 4$ and $5$. It is manifest that the changes in the curves are discontinuous, i.e., curve merging occurs.
• Figure 3: The frequency deviation of the fundamental mode $\Delta\omega=\omega(\epsilon,a)-\omega(0)$ as a function of the bump position $a$, focusing on the post-overtaking stable regime ($a\gtrsim a_{\rm crit}$).
• Figure 4: Scaling relation of the critical position $a_{\rm crit}$ as a function of the perturbation amplitude $\epsilon$, shown for the dCS axial mode with $\beta=1$. The orange data points (from Tab. \ref{['tab:scaling']}) track the value of $a_{\rm crit}$ as $\epsilon$ is varied. The gray dashed line represents the linear fit $a_{\rm crit} = -8.46 \log(\epsilon) + 2.09$. As the perturbation $\epsilon$ decreases to smaller, the critical point $a_{\rm crit}$ is systematically pushed to larger distances.