  Black hole solutions of general relativity exhibit a symmetry for the static
perturbations around these spacetimes, known as "ladder symmetry". This
symmetry proves useful in constructing a tower of solutions for perturbations
and elucidating their general properties. Specifically, the presence of this
symmetry leads to vanishing of the tidal love number associated with black
holes. In this work, we find the most general spherical symmetric and static
black hole spacetime that accommodates this ladder symmetry for scalar
perturbation. Furthermore, we extend our calculations beyond spherical symmetry
to find the class of stationary Konoplya-Rezzolla-Zhidenko black holes, which
also possess a similar ladder structure.
