Paper detail

Supertranslations at Timelike Infinity

We propose a definition of asymptotic flatness at timelike infinity in four spacetime dimensions. We present a detailed study of the asymptotic equations of motion and the action of supertranslations on asymptotic fields. We show that the Lee-Wald symplectic form $Ω(g, δ_1 g, δ_2 g)$ does not get contributions from future timelike infinity with our boundary conditions. As a result, the "future charges" can be computed on any two-dimensional surface surrounding the sources at timelike infinity. We present expressions for supertranslation and Lorentz charges.