Distinguishing fuzzballs from black holes through their multipolar structure

TL;DR

This paper develops a method to analyze the multipolar structure of horizonless microstate geometries, revealing they generally have larger multipole moments than Kerr black holes, which could help distinguish fuzzballs observationally.

Contribution

It introduces a new technique to extract multipole moments from arbitrary stationary spacetimes and applies it to microstate geometries, highlighting their distinct multipolar signatures.

Findings

Microstate geometries often have larger multipole moments than Kerr black holes.

Current measurements of black hole quadrupoles provide mild constraints on fuzzball models.

Future gravitational-wave observations will significantly improve constraints on fuzzball structures.

Abstract

Within General Relativity, the unique stationary solution of an isolated black hole is the Kerr spacetime, which has a peculiar multipolar structure depending only on its mass and spin. We develop a general method to extract the multipole moments of arbitrary stationary spacetimes and apply it to a large family of horizonless microstate geometries. The latter can break the axial and equatorial symmetry of the Kerr metric and have a much richer multipolar structure, which provides a portal to constrain fuzzball models phenomenologically. We find numerical evidence that all multipole moments are typically larger (in absolute value) than those of a Kerr black hole with the same mass and spin. Current measurements of the quadrupole moment of black-hole candidates could place only mild constraints on fuzzballs, while future gravitational-wave detections of extreme mass-ratio inspirals with the space mission LISA will improve these bounds by orders of magnitude.