Are Black Holes Fuzzballs? Probing Horizon-Scale Structure with LISA

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 the fuzzball proposal, a quantum gravity-inspired alternative to Kerr black holes. By introducing generic multipolar deformations encoding potential symmetry breakings and performing a systematic parameter estimation analysis, we forecast LISA's ability to constrain deviations from the Kerr geometry in the near-horizon region. We show that EMRI signals with realistic signal-to-noise ratios can constrain multiple higher-order multipoles at levels orders of magnitude beyond current electromagnetic and ground-based gravitational-wave bounds, opening a new observational window onto horizon-scale structure. In particular, we find that LISA can constrain generic non-axisymmetric mass quadrupole deformations at the $10^{-3}$ level and axisymmetric mass octupole deformations at the $10^{-2}$ level, providing concrete observational targets for identifying fuzzball geometries. Our results demonstrate that precision measurements of EMRI waveforms will transform LISA into a powerful laboratory for fundamental physics and offer the first direct empirical constraints on quantum-gravity-motivated models of compact objects.