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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Veröffentlicht in:	The journal of high energy physics Jg. 2017; H. 11; S. 1 - 44
Hauptverfasser:	De Paoli, Elena, Speziale, Simone
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2017 Springer Nature B.V Springer SpringerOpen
Schlagworte:	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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Abstract	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.
AbstractList	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. 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. 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.
ArticleNumber	205
Author	Speziale, Simone De Paoli, Elena
Author_xml	– sequence: 1 givenname: Elena surname: De Paoli fullname: De Paoli, Elena email: elena.depaoli@uniroma3.it organization: Dipartimento di Fisica, Università di Roma 3, Dipartimento di Fisica, Università di Roma La Sapienza – sequence: 2 givenname: Simone surname: Speziale fullname: Speziale, Simone organization: Aix Marseille Univ., Université de Toulon, CNRS, CPT, UMR 7332
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Snippet	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... We discuss the Hamiltonian dynamics of general relativity with real connection variables on a null foliation, and use the Newman-Penrose formalism to shed... Abstract We discuss the Hamiltonian dynamics of general relativity with real connection variables on a null foliation, and use the Newman-Penrose formalism to...
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SubjectTerms	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
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Title	Sachs’ free data in real connection variables
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