Higher spin dynamics in gravity and $w_{1 + \infty}$ celestial symmetries

Understand

In this paper we extract from a large-$r$ expansion of the vacuum Einstein's equations a dynamical system governing the time evolution of an infinity of higher-spin charges.

• Upon integration, we evaluate the canonical action of these charges on the gravity phase space.
• The truncation of this action to quadratic order and the associated charge conservation laws yield an infinite tower of soft theorems.
• We show that the canonical action of the higher spin charges on gravitons in a conformal primary basis, as well as conformally soft gravitons reproduces the higher spin celestial symmetries derived from the operator product expansion.