Asymptotic conformal symmetry at spatial infinity
arXiv:1910.00520 · doi:10.1103/PhysRevD.100.124051
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.
Some minor changes have been made according to the published version. (previous version comments: The new "twisted Henneaux-Troessaert" parity has been included in the parity conditions and the related results have been presented. Some comments regarding the conformal invariance of the constraints have been added to the subsection on equations of motion.)
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