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 ${ \rm w}_{ 1+\infty}$ charges or soft hair. We relate our results to recent approaches to black hole scattering, including a connection to Wilson lines, $\mathcal{ S}$-matrix results, and celestial holography in curved backgrounds.
Categories: hep-th