Constraints on charged black holes from merger-ringdown signals in GWTC-3 and prospects for the Einstein Telescope

Whether astrophysical black holes (BHs) can have charge is a question to be addressed by observations. In the era of gravitational wave (GW) astronomy, one can constrain the charge of a merged BH remnant using the merger-ringdown signal of the GW data. Extending earlier studies, we analyze five GW events in GWTC-3, assuming Kerr-Newman BHs. Our results show no strong evidence for a charged BH, and give a limit on the charge-to-mass-ratio $Q<0.37$ at 90% credible level. Due to the charge-spin degeneracy in the waveform and the limited signal-to-noise ratios, it is challenging for LIGO/Virgo/KAGRA observations to provide better constraints. We further simulate data for the Einstein Telescope, where signal-to-noise ratios can be as large as $\sim 270$ in the ringdown signal. These simulated events allow us to consider the 220, 221, and 330 ringdown modes altogether, which can help break the charge-spin degeneracy. The analysis of a simulated GW150914-like signal shows that the Einstein Telescope can improve the constraints on the charge-to-mass-ratio to $Q\lesssim 0.2$ at 90% credible level with one ringdown signal.