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

TL;DR

The paper analyzes tidal responses of five-dimensional STU black holes by solving the massless Klein–Gordon equation in the static and near-zone regimes. It shows that static Love numbers depend only on seed Myers–Perry parameters, while dynamical responses acquire boost-dependent signatures through the left/right temperatures encoded in $p$ and $q$, and uses a ladder formalism to connect static solutions and derive conserved currents. A hidden $SL(2,bR)$ Love symmetry in the near-zone is developed, with highest-weight representations explaining vanishing conservative responses in both static and dynamical cases, including near-BPS limits. The work ties these results to holographic perspectives and EFT intuition, and outlines extensions to higher spins, higher dimensions, and quasinormal-mode contexts.

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-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.

Figures (2)

• Figure 1: Contour plot representing the real tidal response coefficients \ref{['Love_n']} for the $\ell=0$ (left) and $\ell=1$ (right), as functions of $y_1$ and $y_2$. We present the results divided by the logarithmic factor $\ln(\varkappa/r^2-r_{-}^2)$, which is independent of $y_1$ and $y_2$, and use the choices $r_{-}=1$, $r_{+}=2$.
• Figure 2: Contour plots representing the dissipative part of response coefficients for the $\ell=0$ (left) and $\ell=1$ (right) cases, as functions of $y_1$ and $y_2$.