Null boundary phase space: slicings, news and memory

TL;DR

This paper constructs a boundary phase space for Einstein gravity with a null boundary, revealing a rich symmetry algebra, integrability conditions, and gravitational memory effects related to wave passage.

Contribution

It introduces a comprehensive boundary phase space framework for null surfaces in Einstein gravity, including symmetry algebra, charge integrability, and memory effects.

Findings

Boundary symmetry algebra is a semi-direct sum of diffeomorphisms and Weyl rescalings.

Surface charges are integrable under specific slicings without graviton flux.

Memory effects encode gravitational wave passage through changes in surface charges.

Abstract

We construct the boundary phase space in $D$-dimensional Einstein gravity with a generic given co-dimension one null surface ${\cal N}$ as the boundary. The associated boundary symmetry algebra is a semi-direct sum of diffeomorphisms of $\cal N$ and Weyl rescalings. It is generated by $D$ towers of surface charges that are generic functions over $\cal N$. These surface charges can be rendered integrable for appropriate slicings of the phase space, provided there is no graviton flux through $\cal N$. In one particular slicing of this type, the charge algebra is the direct sum of the Heisenberg algebra and diffeomorphisms of the transverse space, ${\cal N}_v$ for any fixed value of the advanced time $v$. Finally, we introduce null surface expansion- and spin-memories, and discuss associated memory effects that encode the passage of gravitational waves through $\cal N$, imprinted in a change of the surface charges.