Extrapolating the massive fields to future timelike infinity

TL;DR

This paper studies the asymptotic behavior of massive fields with spins 0, 1, 2 near future timelike infinity in Minkowski spacetime, revealing their decay, oscillations, and the structure of associated symmetry algebras.

Contribution

It introduces a method to extrapolate massive fields to the hyperboloid at future timelike infinity and constructs an extended symmetry algebra including Poincaré and Carrollian diffeomorphisms.

Findings

Massive fields oscillate with frequency equal to their mass.

Fields decay as τ^{-3/2} near future timelike infinity.

The symmetry algebra extends Poincaré to include MDiff and functions on H^3.

Abstract

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 $\tau^{-3/2}$. 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 Poincar\'e charges. The Poincar\'e algebra can be extended to $\text{MDiff}(H^3)\ltimes C^{\infty}(H^3)$ 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.