2014/01/07 by L. Lusanna, M. Villani, Lusanna, L. +2 · 1 citation
Physics and Astronomy · #Cosmology and Gravitation Theories #Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Relativity and Gravitational Theory #astro-ph.CO #gr-qc #hep-th
paper · pdf · doi:10.48550/arxiv.1401.1370
39 pages. arXiv admin note: text overlap with arXiv:0907.4087
arxiv created 2014/01/07 · openalex publication_date 2014/01/07 · arxiv updated 2014/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
By using the York canonical basis of ADM tetrad gravity, in a formulation using radar 4-coordinates for the parametrization of the 3+1 splitting of the space-time, it is possible to write the 4-Riemann tensor of a globally hyperbolic, asymptotically Minkowskian space-time as a Hamiltonian tensor, whose components are 4-scalars with respect to the ordinary world 4-coordinates, plus terms vanishing due to Einstein's equations. Therefore "on-shell" we find the expression of the Hamiltonian 4-Riemann tensor. Moreover, the 3+1 splitting of the space-time used to define the phase space allows us to introduce a Hamiltonian set of null tetrads and to find the Hamiltonian expression of the 4-Ricci scalars of the Newman-Penrose formalism. This material will be used in the second paper to study the 4-Weyl tensor, the 4-Weyl scalars and the four Weyl eigenvalues and to clarify the notions of Dirac and Bergmann observables.