Asymptotic Einstein’s Equations and Celestial Symmetries

Abstract: I will first show how the leading Einstein equations in a large-r expansion around null infinity can be derived and recast in a compact form by relying uniquely on the transformation properties under the corner symmetry group at $\mathcal{I}$, the so-called Weyl BMS group. In addition to the to spin-0 and spin-1 gravitational charges related to the Bondi mass and angular momentum, this analysis reveals the existence of a spin-2 charge, whose Ward identity is equivalent to the sub-subleading soft graviton theorem. Motivated by the infinite towers of soft symmetries recently uncovered in celestial holography, I will extend the recursion relation defining the gravitational charge dynamics to higher spins. I will provide evidence that this recursion relation for higher spin charges corresponds to a truncation of the evolution equations for all subleading terms in the Weyl scalar encoding incoming radiation. Moreover, I will show that these asymptotic charges form a representation of a $w_{1+\infty}$ algebra on the gravitational phase space.

general relativity and quantum cosmologyHEP - theorymathematical physics

Audience: researchers in the topic

MIST High-Energy Theory Seminar