Speaker
Description
The vanishing of static Tidal Love numbers for asymptotically flat black holes in four dimensions has been explained using the "Ladder Symmetry", which is a symmetry for the static perturbation equations around such backgrounds. The existence of a Ladder structure among the solutions is known to be a necessary condition for the Love numbers to vanish. Still, it remains an open question whether it is a sufficient condition for vanishing Love numbers. In this talk, employing the "parametrized formalism for computing tidal Love numbers (as in Phys. Rev. D 109 (2024) 4, 044067)," we will establish that for four-dimensional static, spherically symmetric black-hole spacetimes, and a particular class of stationary rotating four-dimensional black-hole spacetimes (a restricted class of the Konoplya-Rezzolla-Zhidenko spacetimes), any deviation from a Ladder symmetric solution would necessarily result in a non-zero static tidal Love number. In essence, this proves that the existence of Ladder symmetry in the solutions of perturbation equations is a necessary and sufficient condition for the vanishing of static tidal Love numbers in four-dimensional stationary asymptotically-flat black hole solutions belonging to the classes mentioned above.
