Parity violation in photon quasinormal modes of black holes

TL;DR

The paper investigates parity violation in photon quasinormal modes of Schwarzschild black holes endowed with axion hair coupled through a Chern-Simons term. It derives coupled master equations for parity-even and parity-odd gauge-invariant variables with a shared potential $V(r)=f(r) l(l+1)/r^2$ and shows that CS coupling mixes the parities. Using a cosmological axion boundary condition $\phi(t,r)=\phi_c\bigl[t+2M\ln(1-2M/r)\bigr]$ and Leaver's continued fraction method, the work demonstrates a clear splitting of the QNM spectrum into two parity branches when the coupling is nonzero, with existence constrained by $\alpha\phi_c<\sqrt{l(l+1)}/(4M)$. The results suggest that parity-violating electromagnetic signals could serve as a novel probe of the dark sector and motivate extending the analysis to gravitational waves.

Abstract

Given that black holes are ubiquitous in the universe and axion-like scalar fields are potential candidates for dark energy and/or dark matter, it is natural to consider cosmological black holes endowed with axion hair. We investigate the photon quasinormal modes of a Schwarzschild black hole with axion hair where the electromagnetic field is coupled to the axion field via a Chern-Simons interaction. We derive the master equations for the electromagnetic field as a set of coupled equations for parity-even and parity-odd modes and numerically compute quasinormal modes by using Leaver's continued fraction method. We find parity violation in the polarization of photons within the quasinormal mode spectrum. This parity violation in electromagnetic signals could serve as a new probe to explore the nature of the dark sector.

Figures (1)

• Figure 1: The fundamental modes are plotted as a function of the coupling constant. The range of $\alpha\phi_{\rm c}$ is restricted as $\alpha\phi_{\rm c}<\sqrt{l(l+1)}/4M$ by Eq. (\ref{['eq:alphacon']}). The modes with larger imaginary parts $\omega_I$ are plotted with red lines, while those with smaller $\omega_I$ are plotted with blue lines. In the absence of coupling ($\alpha\phi_{\rm c}=0$), these modes are degenerated, but as the coupling increases, we see that the quasinormal modes exhibit parity violation.