Probing fuzzballs and beyond: Model-independent tests of Kerr symmetry breaking with LISA

Abstract

Gravitational waves provide a unique probe of the strong-field regime of gravity, offering access to physics beyond the classical black hole paradigm. We explore how space-based observations of extreme-mass-ratio inspirals (EMRIs) by the Laser Interferometer Space Antenna (LISA) can be used to test for departures from the Kerr geometry, and in particular for the breaking of its axial and equatorial symmetries, as expected in quantum-gravity-inspired alternatives to Kerr black holes such as the fuzzball proposal. By introducing generic multipolar deformations encoding potential symmetry breakings and performing a systematic parameter estimation analysis, we forecast LISA's ability to constrain such departures from the Kerr geometry in the strong-field regime. We show that EMRI signals with realistic signal-to-noise ratios can constrain several higher-order multipoles of the primary, opening a new observational window onto strong-field deviations from the Kerr geometry. In particular, we find that LISA can constrain generic nonaxisymmetric mass quadrupole deformations at the $10^{-4}-10^{-2}$ level and axisymmetric mass octupole deformations at the $10^{-1}$-$10^{0}$ level, providing concrete observational targets for strong-field deviations from the Kerr geometry, such as those that may arise in fuzzball and other exotic-compact-object scenarios. Our results demonstrate that precision measurements of EMRI waveforms will transform LISA into a powerful laboratory for fundamental physics and offer precise constraints on quantum-gravity-motivated models of compact objects.