Extrapolating the massive fields to future timelike infinity

A bstract It is well-known that future timelike infinity ( i + ) in four-dimensional Minkowski spacetime is conformal to the unit three-dimensional hyperboloid ( H 3 ). We asymptotically expand massive fields with spin 0 , 1 , 2 near i + and extrapolate them onto this hyperboloid. These fields oscillate with a frequency equal to their mass and exhibit a universal asymptotic decay τ − 3 / 2 . The fundamental fields are free and encode the outgoing scattering data. They are local operators defined on the boundary H 3 with which we construct the Poincaré charges. The Poincaré algebra can be extended to MDiff( H 3 ) ⋉ C ∞ ( H 3 ) using smeared operators associated with energy and angular momentum densities. For spinning fields, a spin operator must be included to close the algebra. The extended algebra shares the same form as the five-dimensional intertwined Carrollian diffeomorphism and reduces to the BMS algebra at i + by restricting the choice of test functions and vectors.