Ladder Symmetries of Higher Dimensional Black Holes

TL;DR

This paper develops ladder operators for static tidal perturbations of higher-dimensional black holes, revealing why their Love numbers vanish for certain multipole and dimensional combinations, extending previous 4D results.

Contribution

It introduces ladder operators for higher-dimensional black hole perturbations, explaining the vanishing Love numbers through a generalized symmetry framework.

Findings

Ladder operators connect solutions at different multipole orders.

The vanishing Love numbers are explained by the ladder structure and ground state solutions.

The work extends the symmetry explanation of Love number vanishing from 4D to higher dimensions.

Abstract

We compute the ladder operators for static tidal perturbations to higher-dimensional black holes. These operators map between solutions of the relevant equation of motion at different multipole orders. We focus on spin 0, 1 and 2 perturbations to the Schwarzschild-Tangherlini black hole and on spin 0 perturbations to the 5D Myers-Perry black hole. The ladder structure, used in conjunction with the existence of special ground state solutions, explains why the Love numbers of these higher-dimensional black holes vanish for specific combinations of the multipole moment and number of spacetime dimensions. This generalizes previous work on a ladder symmetry explanation for the vanishing of 4D black hole static Love numbers to higher dimensions.