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Black hole solutions of general relativity exhibit a symmetry for the staticperturbations around these spacetimes, known as ``ladder symmetry''. Thissymmetry proves useful in constructing a tower of solutions for perturbationsand elucidating their general properties. Specifically, the presence of thissymmetry leads to vanishing of the tidal love number associated with blackholes. In this work, we find the most general spherical symmetric and staticblack hole spacetime that accommodates this ladder symmetry for scalarperturbation. Furthermore, we extend our calculations beyond spherical symmetryto find the class of stationary Konoplya-Rezzolla-Zhidenko black holes, whichalso possess a similar ladder structure.

Symmetries of Love: Ladder Structure of Static and Rotating Black Holes