The multipolar structure of fuzzballs

TL;DR

This paper develops a method to analyze the multipolar structure of fuzzball microstate geometries, revealing they often have larger and more complex multipole moments than Kerr black holes, with implications for observational tests.

Contribution

It introduces a refined technique to extract multipole moments of stationary spacetimes and applies it to a broad class of fuzzball solutions, highlighting their richer structure compared to black holes.

Findings

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

Multipole moments grow monotonically with microstate size, with a minimum at the black-hole limit.

Microstates break axial and equatorial symmetry, leading to complex multipolar structures.

Abstract

We extend and refine a general method to extract the multipole moments of arbitrary stationary spacetimes and apply it to the study of a large family of regular horizonless solutions to $ {\cal N}{\,=\,}2$ four-dimensional supergravity coupled to four Abelian gauge fields. These microstate geometries can carry angular momentum and have a much richer multipolar structure than the Kerr black hole. In particular they break the axial and equatorial symmetry, giving rise to a large number of nontrivial multipole moments. After studying some analytical examples, we explore the four-dimensional parameter space of this family with a statistical analysis. We find that microstate mass and spin multipole moments are typically (but not always) larger that those of a Kerr black hole with the same mass and angular momentum. Furthermore, we find numerical evidence that some invariants associated with the (dimensionless) moments of these microstates grow monotonically with the microstate size and display a global minimum at the black-hole limit, obtained when all centers collide. Our analysis is relevant in the context of measurements of the multipole moments of dark compact objects with electromagnetic and gravitational-wave probes, and for observational tests to distinguish fuzzballs from classical black holes.