Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2005-08-20
Class.Quant.Grav. 23 (2006) 2841-2848
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Final version with additional references
Scientific paper
10.1088/0264-9381/23/9/005
Ten conservation laws in useful polynomial form are derived from a Cartan form and Exterior Differential System (EDS) for the tetrad equations of vacuum relativity. The Noether construction of conservation laws for well posed EDS is introduced first, and an illustration given, deriving 15 conservation laws of the free field Maxwell Equations from symmetries of its EDS. The Maxwell EDS and tetrad gravity EDS have parallel structures, with their numbers of dependent variables, numbers of generating 2-forms and generating 3-forms, and Cartan character tables all in the ratio of 1 to 4. They have 10 corresponding symmetries with the same Lorentz algebra, and 10 corresponding conservation laws.
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