  Expanding around null hypersurfaces, such as generic Kerr black hole
horizons, using co-rotating Kruskal-Israel-like coordinates we study the
associated surface charges, their symmetries and the corresponding phase space
within Einstein gravity. Our surface charges are not integrable in general.
Their integrable part generates an algebra including superrotations and a
BMS_3-type algebra that we dub "T-Witt algebra". The non-integrable part
accounts for the flux passing through the null hypersurface. We put our results
in the context of earlier constructions of near horizon symmetries, soft hair
and of the program to semi-classically identify Kerr black hole microstates.
