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

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-Nordström, 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.

💡 Research Summary

This paper presents a comprehensive study of the tidal response of the most general five‑dimensional charged rotating black holes that arise in the STU model of N=2 supergravity (the so‑called STU black holes). These solutions are characterized by a mass parameter, two independent angular momenta, and up to three independent U(1) charges. By solving the massless Klein‑Gordon equation on this background and separating variables, the authors obtain angular and radial wave equations. In the static limit (zero frequency) the radial solution behaves as (R_\ell(r)\sim A_\ell r^\ell + B_\ell r^{-(\ell+3)}); the ratio (B_\ell/A_\ell) encodes the (real) Love numbers, while its imaginary part gives the dissipative coefficients. Unlike four‑dimensional general relativity, where static Love numbers vanish universally, the five‑dimensional case yields non‑zero static Love numbers for generic parameters, reflecting the altered balance between gravitational attraction and centrifugal repulsion in higher dimensions.

For dynamical perturbations (non‑zero frequency) the authors perform a matched‑asymptotic expansion, separating a near‑zone region ((r\ll 1/\omega)) from a far‑zone region. They derive explicit expressions for the frequency‑dependent Love numbers and dissipation coefficients. A particularly striking result is obtained in the BPS limit, where the boost parameters (\delta_i) are taken to infinity while keeping the charge‑to‑mass ratios fixed. In this limit the Love numbers and dissipative coefficients become frequency‑independent and identically zero, indicating that supersymmetric extremal black holes do not develop tidal deformations even dynamically.

A major technical advance of the work is the construction of a ladder (raising‑lowering) operator formalism for the static radial equation. By factorizing the second‑order radial operator into a product of first‑order operators (L_-) and (L_+), the authors generate a hierarchy of solutions connecting different multipole orders (\ell). This ladder structure yields conserved Noether currents that reproduce the ADM mass, the two angular momenta, and the three electric charges, thereby extending the known four‑dimensional ladder symmetry to five dimensions where the operators depend non‑trivially on both rotation parameters and charge boost parameters.

In the near‑zone regime the radial equation simplifies to a form invariant under an (sl(2,\mathbb{R})) symmetry. The authors explicitly construct the three generators (H_0, H_{\pm}) and verify the algebra (