Asymptotic conformal symmetry at spatial infinity

TL;DR

This paper explores how adding spatial conformal symmetry to the asymptotic symmetry group of certain spacetimes affects boundary conditions, conserved charges, and physical quantities like mass, revealing new effects and invariances.

Contribution

It demonstrates that only dilations preserve boundary conditions under hypersurface deformations when adding spatial conformal symmetry, and analyzes their impact on conserved charges and physical quantities.

Findings

Dilation generators preserve boundary conditions under hypersurface deformations.

Conserved dilation charge includes nonzero, field-independent terms.

Conformal symmetry modifies the ADM mass of the spacetime.

Abstract

In this paper, the effects of adding spatial conformal symmetry to the asymptotic symmetry group of an asymptotically conformally flat spacetime are studied. It is shown that, in addition to the BMS group, only the dilations of the spatial conformal generators keep the corresponding boundary conditions conformally invariant under hypersurface deformations. We prove that in order to attain (i) a well-defined symplectic structure and (ii) a finite and (iii) integrable conserved charge, these conditions are satisfied simultaneously when admitting Regge-Teitelboim and twisted Henneaux-Troessaert parity conditions, where the latter also contain supertranslation invariance. The conserved dilation charge contains nonzero terms independent of the field variables, giving a nonvanishing effect on the boundary. The dilation symmetry also modifies the ADM mass, which is another physical effect of the conformal symmetry.