Self-dual black holes in celestial holography

Abstract We construct two-dimensional quantum states associated to four-dimensional linearized rotating self-dual black holes in (2, 2) signature Klein space. The states are comprised of global conformal primaries circulating on the celestial torus, the Kleinian analog of the celestial sphere. By introducing a generalized tower of Goldstone operators we identify the states as coherent exponentiations carrying an infinite tower of w1+∞ charges or soft hair. We relate our results to recent approaches to black hole scattering, including a connection to Wilson lines, $$ \mathcal{S} $$ S -matrix results, and celestial holography in curved backgrounds.