New Near Extremal Black Holes and Love Symmetry

Abstract: Rotating and charged black holes are known to exhibit remarkable properties close to extremality, including emergent hidden symmetries and holographic duality to 2D theories. In this note, we introduce a new class of near-extremal black holes living in $(2,2)$ signature, strongly resembling the Lorentzian ones but with an exact integrable structure $SL(2,\mathbb{R})\times SL(2,\mathbb{R})$. The exterior of the black hole is a self-dual solution with a photon ring. It develops an infinite near-horizon throat described by the Eguchi-Hanson instanton. An exact version of the so-called Love symmetry controls perturbations on the throat. Furthermore, the normalizable spectrum of this black hole provides quasinormal modes in Lorentzian signature.