A new study has explored how the quasinormal modes (QNM) of black holes, the "waves" they emit after a perturbation, can be used to infer the properties of these objects and the surrounding spacetime. The work compares two approaches: one based on a specific metric model (the Konoplya-Rezzolla-Zhidenko parametrization) and another "agnostic" to the metric, which focuses on local properties near the light ring. Both models were applied to simulated data and the real gravitational wave observation GW250114, showing consistency with the Kerr metric of general relativity.

The research connects a calibrated eikonal method, which relates quasinormal mode shifts to local metric properties near the light ring, with the underlying rotating black hole metric. Using Bayesian inference, both one-parameter and simultaneous multi-parameter analyses were performed. It was found that uniform priors on the metric-specific coefficients can induce strongly nonuniform and skewed priors on these local metric quantities. However, for data injections compatible with general relativity, both models remain consistent with Kerr and yield similar posteriors for the orbital frequency and Lyapunov exponent.

For scenarios representing deviations from general relativity, one-parameter analyses can fail to recover the injected local deviations, and in the metric-specific case, can bias the global metric reconstruction. Multi-parameter analyses of both models, while introducing degeneracies and differences in marginalized parameters, yield consistent constraints, suggesting sufficient robustness. The application of this framework to approximate posterior information from the ringdown analysis of GW250114 confirms that both models are consistent with the Kerr metric in general relativity, strengthening our understanding of these extreme phenomena.