Sachs’ free data in real connection variables
High Energy Physics - Theory
coupling: nonminimal
fermion
FOS: Physical sciences
QC770-798
General Relativity and Quantum Cosmology (gr-qc)
algebra
01 natural sciences
General Relativity and Quantum Cosmology
Nuclear and particle physics. Atomic energy. Radioactivity
0103 physical sciences
Models of Quantum Gravity
general relativity
Bianchi identity
[PHYS.GRQC] Physics [physics]/General Relativity and Quantum Cosmology [gr-qc]
mathematical methods
stability
boundary condition
Hamiltonian
space-time
foliation
High Energy Physics - Theory (hep-th)
twist
field theory: vector
[PHYS.HTHE] Physics [physics]/High Energy Physics - Theory [hep-th]
Classical Theories of Gravity
geodesic
DOI:
10.1007/jhep11(2017)205
Publication Date:
2017-12-01T10:09:47Z
AUTHORS (2)
ABSTRACT
Abstract
We discuss the Hamiltonian dynamics of general relativity with real connection variables on a null foliation, and use the Newman-Penrose formalism to shed light on the geometric meaning of the various constraints. We 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. A pair of second-class constraints reduces these connection components to the shear of a null geodesic congruence, thus establishing equivalence with the second-order formalism, which we show in details at the level of symplectic potentials. 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; the same one that allows one to describe the radiative data at future null infinity in terms of a shear of a (non-geodesic) asymptotic null vector field in the physical spacetime. Finally, we compute the modification to the spin coefficients and the null congruence in the presence of torsion.
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