Multipole Ratios: A New Window into Black Holes

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.

Figure 1

Multipole ratios $R(L)\equiv M_{L/2}{M}_{3L/2}/M_L^2$ (even $L$) in the geometry $C$, calculated using the direct BPS method (in red) and the indirect method (in blue).