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Reformulate EMRI mapping via source multipoles

Reformulate the spacetime mapping problem for extreme-mass-ratio inspirals in terms of the source (horizon) multipole moments of the massive black hole, and determine how these source moments can be inferred from the gravitational-wave signal.

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Background

In EMRIs, the small body effectively maps the geometry near the massive black hole. Traditional approaches focus on field multipoles observable at infinity, but the review shows that near-horizon geometry is determined by source (horizon) multipoles via characteristic evolution, and that BH Love numbers for field moments vanish while horizon Love numbers do not.

A source-multipole-based mapping could provide a robust way to test Kerrness and discern near-horizon structure directly from the GW signal.

References

Open Issue 11 (OI-11) In an extreme mass ratio system, the small compact object ``maps'' the spacetime around the massive black hole and the emitted GW signal can potentially be used to test the Kerr nature of the massive black hole by measuring its field multipole moments . As the discussion in this sub-section shows, in the perturbative regime, the spacetime geometry is determined by the source mutipole moments. Therefore we are led to ask: Can the spacetime mapping problem be reformulated in terms of the source multipole moments?

— Quasi-Local Black Hole Horizons: Recent Advances (2502.11825 - Ashtekar et al., 17 Feb 2025) in Section 6.3