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Ladder Symmetries of Higher Dimensional Black Holes

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.

preprint2026arXivOpen access
Roman BerensLam HuiDaniel McLoughlinAdam R. SolomonJohn Staunton
gr-qchep-th
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Roman BerensLam HuiDaniel McLoughlinAdam R. SolomonJohn Staunton

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