Probing Kerr symmetry breaking with LISA: Extreme-mass-ratio inspirals
Phys. Rev. D 114, 064010 – Published 4 September, 2026
DOI: https://doi.org/10.1103/l12t-9c9m
Abstract
Extreme-mass-ratio inspirals (EMRIs) are one of the main sources of gravitational waves expected in the low-frequency band, where space-based detectors like Laser Interferometer Space Antenna (LISA) will operate. The large number of gravitational-wave cycles accumulated in the EMRI signal in the strong-field regime makes them very precise probes of the local spacetime geometry that are highly sensitive to deviations from the Kerr black hole paradigm. In this work, we investigate EMRIs around generic, non-Kerr compact objects characterized by an arbitrary and rich multipolar structure. At leading post-Newtonian and linear mass-ratio orders, we incorporate in the waveform model both the axisymmetric and nonaxisymmetric components of the mass quadrupole and octupole moments, parametrizing in this way the breaking of two fundamental symmetries of the Kerr metric. We study the impact of these modifications on the waveform following the philosophy of the EMRI analytic kludge models. In our case, the orbital evolution follows from Lagrangian that contains of the multipolar structure of the primary, including for the first time the nonaxisymmetric multipole moments that break axial symmetry. Then, using Fisher-matrix analysis, we assess the capability of LISA to constrain deviations of the multipole moments from their Kerr values and, in particular, the possibility of detecting symmetry-breaking effects. In this way, we analyze how effectively LISA will be able to probe models beyond General Relativity that predict horizon-scale modifications, such as the fuzzball model proposed in string theory. Our results demonstrate that future LISA observations of EMRIs will provide powerful and unprecedented tests of black hole structure and the underlying theory of gravity. In particular, with one year of LISA data from the inspiral of a compact object into a rotating supermassive black hole of and signal-to-noise ratio of 30, it will be possible to place tight bounds on deviations from the two fundamental symmetries of the Kerr metric, constraining equatorial symmetry breaking in the mass multipole sector to the level and axial symmetry breaking to the level.
