CENTRA Seminar - Sachs’ constraint-free data in real connection variables - 31 janeiro 2019

Simone Speziale

Centre de Physique Théorique de Luminy, Marseille

We present the Hamiltonian dynamics of general relativity with real connection variables on a null foliation, and identify the equivalent of Sachs' constraint-free initial data as projections of connection components related to null rotations, i.e. the translational part of the ISO(2) group stabilising the internal null direction soldered to the hypersurface. We show how the metric formalism is recovered in the absence of torsion, and how the latter modifies the spin coefficients and null congruences. A special feature of the first-order formulation is that Sachs' propagating equations for the shear, away from the initial hypersurface, are turned into tertiary constraints; their role is to preserve the relation between connection and shear under retarded time evolution. The conversion of wave-like propagating equations into constraints is possible thanks to an algebraic Bianchi identity, which we show is the same that is at work at future null infinity to grant equivalence between Sachs’ symplectic structure and the one by Ashtekar and Streubel. We conclude with possible applications for loop quantum gravity.