We compute the gravitational multipole moments and ratios of moments of nonextremal and of supersymmetric black holes in four dimensions, as well as of horizonless microstate geometries of the latter. For supersymmetric and for Kerr black holes many of these multipole moments vanish, and their dimensionless ratios are ill defined. We present two methods to compute these dimensionless ratios, which for certain supersymmetric black holes agree surprisingly well. We also compute these dimensionless ratios for the Kerr solution. Our methods allow us to calculate an infinite number of hitherto unknown parameters of Kerr black holes, giving us a new window into their physics.

中文翻译：

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多极比：通向黑洞的新窗口

我们在四个维度上计算引力多极矩以及非极端黑洞和超对称黑洞的矩比率，以及后者的无水平微态几何形状。对于超对称和Kerr黑洞，这些多极矩中的许多消失了，并且它们的无量纲比也没有定义。我们提出了两种计算这些无量纲比率的方法，对于某些超对称黑洞，它们令人惊讶地达成了一致。我们还为Kerr解决方案计算了这些无量纲比率。我们的方法使我们能够计算无限数量的迄今未知的Kerr黑洞参数，为我们提供了一个了解其物理学的新窗口。