In contrast to the Einstein-Hilbert action, the action for self-dual gravity contains vierbeins. They are eleminated at the level of observables by an SL(2, ℂ) gauge condition implied by the action. We argue that despite this condition, new “edge” or superselected state vectors corresponding to maps of the spheres S∞2 at infinity to SL(2, ℂ) arise. They are characterised by new quantum numbers and they lead to mixed states. For black holes, they arise both at the horizon and the spatial infinity and may be relevant for the black hole information paradox. Similar comments can be made about the EinsteinPalatini action which uses vierbeins.
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