Multipole Ratios: A New Window into Black Holes.

Iosif Bena,Daniel R. Mayerson

doi:10.1103/physrevlett.125.221602

Abstract

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.

Highlights

Introduction.—There is an extended literature that argues that in order for black hole evaporation to be consistent with quantum unitarity, there should exist a structure at the scale of the horizon of the black hole [1,2]
Understanding how the physics of this structure differs from the physics of the black hole is of crucial importance, especially in the light of the recent observations of gravitational waves emitted when two black holes merge [10], and of future experiments that plan to explore extreme mass-ratio inspiral (EMRI) gravity waves [11] that should reveal very detailed information about horizon-scale physics
One important way in which microstate geometries differ from the black hole is in the higher multipole moments of the mass and angular momentum

Summary

Published by the American Physical Society

Ratios in the scaling limit of various microstate geometries, we obtain a whole set of new quantities that characterize the BPS black hole We will call this method of computing multipole ratios the “direct BPS” method. We can use the indirect method to compute multipole ratios that are undefined for the Kerr black hole: one can deform it into a general charged STU black hole, compute multipole ratios, and take back the charges to zero. In this way, we can associate well-defined multipole ratios with the Kerr black hole. Axisymmetric spacetimes with Killing vectors ∂t; ∂φ [for which the ðl; mÞ multipoles are only nonzero for m 1⁄4 0], the asymptotic expansion of the metric components involving t in an ACMC-∞ coordinate system are given by gtt 1⁄4

Sl l

The moduli of the solutions we construct are

Its values for the three solutions we consider is