Researchers show that future space-based gravitational-wave observations with the Laser Interferometer Space Antenna (LISA) can search for small departures from the standard black hole picture known as fuzzballs. The fuzzball proposal, motivated by string theory, replaces the classical event horizon with a quantum region that can have structure at the same scale as the would-be horizon. The authors forecast that LISA observations of extreme-mass-ratio inspirals (EMRIs) could constrain some of those horizon-scale deviations to very small levels.

A fuzzball is an alternative to the usual Kerr black hole. Instead of a smooth event horizon, individual microstates are horizonless, extended geometries that share the same total mass and spin but differ close to where the horizon would be. Those differences can break the spacetime symmetries of Kerr black holes, for example by making the mass distribution non-axisymmetric or by breaking equatorial symmetry. If such structure exists, it could leave a measurable imprint on the gravitational waves from a small object spiraling into a much larger compact object.

To test this, the authors built a semi-analytic EMRI waveform model that expands the central object’s gravitational field in multipole moments. They promote some of those multipoles to independent parameters to encode possible symmetry breaking. The model is 20-dimensional and treats the inspiral at leading order in the small mass ratio, using an effective one-body description for the orbital motion and a quadrupole approximation for gravitational radiation. The paper focuses on non-axisymmetric components of the mass quadrupole and on the axisymmetric mass octupole as concrete probes of the two basic symmetries of Kerr spacetime.

Using this framework, the authors perform parameter-estimation forecasts for realistic LISA signal strengths. They find that EMRIs could constrain non-axisymmetric mass-quadrupole deformations down to about 10^-3, and axisymmetric mass-octupole deformations down to about 10^-2. These projected limits are many orders of magnitude tighter than current constraints from electromagnetic observations and ground-based gravitational-wave detectors. Because EMRIs can spend tens of thousands to millions of cycles in the LISA band, their waveforms carry very detailed information about the near-horizon geometry, making them especially sensitive probes.