Sachs’ free data in real connection variables

• DOI: 10.1007/jhep11(2017)205
• Publication Date: 2017-12-01T10:09:47Z
• Authors: Elena De Paoli; Simone Speziale
• Keywords: Hypersurface

A bstract We discuss the Hamiltonian dynamics of general relativity with real connection variables on a null foliation, and use Newman-Penrose formalism to shed light geometric meaning various constraints. identify equivalent Sachs’ constraint-free initial data as projections components related rotations, i.e. translational part ISO(2) group stabilising internal direction soldered hypersurface. pair second-class constraints reduces these shear geodesic congruence, thus establishing equivalence second-order formalism, which we show in details at level symplectic potentials. special feature first-order formulation is that propagating equations for shear, away from hypersurface, are turned into tertiary constraints; their role preserve relation between under retarded time evolution. The conversion wave-like possible thanks an algebraic Bianchi identity; same one allows describe radiative future infinity terms (non-geodesic) asymptotic vector field physical spacetime. Finally, compute modification spin coefficients congruence presence torsion.