re-soft-hair | Parallel Transport

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.

Replies

Keefe Mitman

replied on Twitter with

By supertranslation-like things I was also thinking of the Virasoro algebra (which is where soft hairs comes from; see, e.g., arxiv.org/abs/1810.01847)

Keefe Mitman

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But they are special diffeomorphisms in the sense that they are large diffeomorphisms so they act non-trivially on the boundary. I guess it depends on what people mean by “physically inequivalent”.

Kartik Prabhu

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Not sure what that has to do with anything. Any diffeo, special or not, does not change the geometry.

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”!

👻 ghouLeo C. frankenStein 🧟

replied on Twitter with

Ok, so I don’t understand how something you said earlier jives with this comment. Both an event horizon and scri have diffeos — so in what sense is the symmetry group of scri smaller? Because there is a ‘universal structure’ that can be fixed at scri? But there is no universal

👻 ghouLeo C. frankenStein 🧟

replied on Twitter with

I wish I had a geometric understanding of these extensions to the bms algebra. I know their charge integrals are finite so something makes *algebraic* sense, but I have no idea what it corresponds to geometrically.

Kartik Prabhu

replied on Twitter with

There is nothing going on with these extended “symmetries”. If you give me a random thing to call a symmetry I can easily make up a charge formula for you.