Tidal perturbations and Love Symmetry for five-dimensional charged rotating black holes

TL;DR

This paper studies the tidal responses and Love symmetries of five-dimensional charged rotating black holes, revealing new conditions for Love number vanishing and developing a novel ladder formalism for static solutions.

Contribution

It introduces a ladder formalism for 5D black holes, derives Love numbers and dissipation coefficients, and uncovers Love symmetry via an $sl(2, {R})$ algebra.

Findings

Love numbers vanish under certain conditions in 5D black holes.

A new ladder formalism for static solutions is developed.

Love symmetry is shown to explain Love-number vanishing.

Abstract

We investigate the tidal response of general five-dimensional (5D) black holes of STU supergravity, which include as special cases important solutions such as the Myers-Perry, BMPV, 5D Reissner-Nordstr\"om, Kerr-Newman and dyonic black holes. Solutions are parameterized by their mass, two angular momenta and up to three $U(1)$ charges. Love numbers and dissipation coefficients are obtained in the static and dynamic cases. In the latter scenario, we find new, nontrivial conditions, realized in important limiting cases of the theory, such as the BPS limit, where frequency-independent vanishing conditions are obtained. We also develop a ladder formalism for static solutions and derive the conserved charges. To the best of our knowledge, this formalism had not been previously derived for 5D black holes, including neutral ones. Finally, we show the emergence of Love symmetry in the near-zone regime, and derive the generators of the associated $sl(2,\mathbb{R})$ algebra. It is shown that all conditions for Love-number vanishing can be explained by this algebra in terms of the highest-weight property.