Sachs’ free data in real connection variables

A bstract 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 project...

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Vydáno v:	The journal of high energy physics Ročník 2017; číslo 11; s. 1 - 44
Hlavní autoři:	De Paoli, Elena, Speziale, Simone
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2017 Springer Nature B.V Springer SpringerOpen
Témata:	Classical and Quantum Gravitation Classical Theories of Gravity Elementary Particles Equivalence Formalism General Relativity and Quantum Cosmology High energy physics High Energy Physics - Theory Models of Quantum Gravity Physics Physics and Astronomy Quantum Field Theories Quantum Field Theory Quantum Physics Real variables Regular Article - Theoretical Physics Relativity Relativity Theory Shear String Theory Wave propagation Classical Theories of Gravity Models of Quantum Gravity fermion boundary condition space-time algebra general relativity foliation Bianchi identity coupling: nonminimal geodesic mathematical methods twist Hamiltonian field theory: vector stability
ISSN:	1029-8479, 1126-6708, 1029-8479
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Shrnutí:	A bstract 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.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	1029-8479 1126-6708 1029-8479
DOI:	10.1007/JHEP11(2017)205