Null boundary phase space: slicings, news & memory
H. Adami, Daniel Grumiller, M. M. Sheikh-Jabbari, V. Taghiloo, Hossein Yavartanoo, Céline Zwikel
Abstract
A bstract We construct the boundary phase space in D -dimensional Einstein gravity with a generic given co-dimension one null surface $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> as the boundary. The associated boundary symmetry algebra is a semi-direct sum of diffeomorphisms of $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> and Weyl rescalings. It is generated by D towers of surface charges that are generic functions over $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> . These surface charges can be rendered integrable for appropriate slicings of the phase space, provided there is no graviton flux through $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> . In one particular slicing of this type, the charge algebra is the direct sum of the Heisenberg algebra and diffeomorphisms of the transverse space, $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> 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 $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> , imprinted in a change of the surface charges.