Asymptotic symmetries and charges at spatial infinity in general relativity

Understand

We analyze the asymptotic symmetries and their associated charges at spatial infinity in $4$-dimensional asymptotically-flat spacetimes.

• We use the covariant formalism of Ashtekar and Hansen where the asymptotic fields and symmetries live on the $3$-manifold of spatial directions at spatial infinity, represented by a timelike unit-hyperboloid (or de Sitter space).
• Using the covariant phase space formalism, we derive formulae for the charges corresponding to asymptotic supertranslations and Lorentz symmetries at spatial infinity.
• With the motivation of, eventually, proving that these charges match with those defined on null infinity -- as has been conjectured by Strominger -- we do not impose any restrictions on the choice of conformal factor in contrast to previous work on this problem.