Bianchi Massimo, Consoli Dario, Grillo Alfredo, Morales Josè Francisco, Pani Paolo, Raposo Guilherme
Dipartimento di Fisica, Universit di Roma "Tor Vergata" and Sezione INFN Roma2, Via della ricerca scientifica 1, 00133, Roma, Italy.
Mathematical Physics Group, University of Vienna, Boltzmanngasse 5 1090 Vienna, Austria.
Phys Rev Lett. 2020 Nov 27;125(22):221601. doi: 10.1103/PhysRevLett.125.221601.
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.
在广义相对论中，孤立黑洞的唯一静态解是克尔时空，它具有仅取决于其质量和自旋的特殊多极结构。我们开发了一种通用方法来提取任意静态时空的多极矩，并将其应用于大量无视界微观态几何结构。后者可以打破克尔度规的轴向和赤道对称性，并具有更丰富的多极结构，这为从现象学上约束模糊球模型提供了一个途径。我们发现数值证据表明，所有多极矩（绝对值）通常都比具有相同质量和自旋的克尔黑洞的多极矩更大。目前对黑洞候选体四极矩的测量对模糊球只能施加适度的约束，而未来利用空间任务LISA对极端质量比吸积的引力波探测将使这些界限提高几个数量级。
