Kartik Prabhu
replied to a post on Twitter with
I don’t know what “soft hair” means and what it has to do with supertranslations. Null infinity is “less” symmetric than a horizon; it has a smaller symmetry group since null infinity has much more structure due to everything falling-off. Supertranslations do not change the geometry, they are diffeomorphisms and just like any diffeomorphism they do not change the local geometry.
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Kartik Prabhu
replied on Twitter with
Those are not even continuous vector fields and don’t even preserve the manifold structure of the spacetime. So not sure why they are “symmetries”. If you are allowed those kinds of vector fields then might as well take a delta function vector field and call it “ultra soft hair”!