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.

中文翻译：

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通过黑洞的多极结构区分模糊球

在广义相对论中，孤立的黑洞的唯一平稳解是Kerr时空，它具有独特的多极结构，仅取决于其质量和自旋。我们开发了一种通用方法来提取任意平稳时空的多极矩，并将其应用于一大批无水平微态几何。后者可以破坏Kerr度量的轴向和赤道对称性，并具有更丰富的多极结构，这为从现象学角度上限制Fuzzball模型提供了一个门户。我们发现了数值证据，所有多极矩通常（在绝对值上）大于具有相同质量和自旋的Kerr黑洞的矩。目前对黑洞候选者的四极矩的测量只能对模糊球施加轻微的约束，LISA将把这些界限提高几个数量级。