Exploring Ladder Symmetry and Love Numbers for Static and Rotating Black Holes

TL;DR

This paper investigates the ladder symmetry in static and rotating black holes, revealing its implications for tidal Love numbers and extending the symmetry to more general black hole solutions.

Contribution

It identifies the most general static spherically symmetric black hole with ladder symmetry and extends the analysis to stationary black holes with similar properties.

Findings

Ladder symmetry leads to vanishing tidal Love numbers.

The most general static spherically symmetric black hole with ladder symmetry is characterized.

Stationary black holes with ladder structure are identified.

Abstract

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.