Black Hole Fine Structure

In General Relativity, axial and polar black-hole perturbations share identical quasinormal-mode spectra, a property known as isospectrality. New physics can break this degeneracy, producing a spectral splitting analogous to atomic fine structure. We perform a theory-agnostic search for such splitting in gravitational-wave observations. We find no evidence for isospectrality breaking and place a combined $90\mathrm{\%}$ upper limit of $<28.5\mathrm{\%}$ on the relative frequency splitting. We map these constraints onto several modified-gravity theories, constraining the coupling-lengths to be $\lesssim 28\mathrm{k}\mathrm{m}$.