Near-Zone Symmetries of Kerr Black Holes

TL;DR

This paper investigates the near-zone symmetries of scalar fields around Kerr black holes, unifies them under an SO(4,2) group, and explores their implications for static sector symmetries and Love numbers.

Contribution

It provides a geometric framework unifying recent symmetry discoveries as part of an SO(4,2) group and analyzes their role in black hole physics.

Findings

Symmetries form an SO(4,2) group structure.

Subset of symmetries are exact in the static sector.

Symmetries explain the vanishing of Love numbers.

Abstract

We study the near-zone symmetries of a massless scalar field on four-dimensional black hole backgrounds. We provide a geometric understanding that unifies various recently discovered symmetries as part of an SO(4,2) group. Of these, a subset are exact symmetries of the static sector and give rise to the ladder symmetries responsible for the vanishing of Love numbers. In the Kerr case, we compare different near-zone approximations in the literature, and focus on the implementation that retains the symmetries of the static limit. We also describe the relation to spin-1 and 2 perturbations.