Love symmetry

Understand

Perturbations of massless fields in the Kerr-Newman black hole background enjoy a (``Love'') SL$(2,\mathbb{R})$ symmetry in the suitably defined near zone approximation.

• We present a detailed study of this symmetry and show how the intricate behavior of black hole responses in four and higher dimensions can be understood from the SL$(2,\mathbb{R})$ representation theory.
• In particular, static perturbations of four-dimensional black holes belong to highest weight SL$\left(2,\mathbb{R}\right)$ representations.
• It is this highest weight property that forces the static Love numbers to vanish.