Conserved quantities of the gravitational field in tetrad notation

Abstract

We reexpress in tetrad form the background dependent family of superpotentials for the first-order Lagrangians which generate Einstein’s field equations, found in an earlier paper. Using a result on the pull-back properties of the Poincar´eCartan forms for second-order Lagrangian field theories, we show that these superpotentials are the superpotentials corresponding to a Lorentz invariant family of first-order tetrad Lagrangians.

Keywords

• general relativity
• conservation laws