Conservation laws for vacuum tetrad gravity
Frank B. Estabrook
TL;DR
This paper derives ten conservation laws for vacuum tetrad gravity using Cartan forms and Exterior Differential Systems, paralleling Maxwell equations, and introduces a Noether-based method for well-posed EDS.
Contribution
It presents a novel derivation of conservation laws for vacuum tetrad gravity through Cartan forms and EDS, paralleling Maxwell equations, and introduces a Noether construction for well-posed EDS.
Findings
Derived 10 conservation laws for vacuum tetrad gravity.
Established structural parallels between Maxwell EDS and gravity EDS.
Introduced a Noether construction method for conservation laws in EDS.
Abstract
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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