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We report off-shell Noether currents obtained from off-shell Noether potentials for first-order general relativity described by n-dimensional Palatini and Holst Lagrangians including the cosmological constant. These off-shell currents and potentials are achieved by using the corresponding Lagrangian and the off-shell Noether identities satisfied by diffeomorphisms generated by arbitrary vector fields, local S O (n) or S O (n− 1, 1) transformations,‘improved diffeomorphisms’, and the ‘generalization of local translations’ of the orthonormal frame and the connection. A remarkable aspect of our approach is that we do not use Noether’s theorem in its direct form. By construction, the currents are off-shell conserved and lead naturally to the definition of off-shell Noether charges. We also study what we call the ‘half off-shell’case for both Palatini and Holst Lagrangians. In particular, we find that the resulting diffeomorphism and local S O (3, 1) or S O (4) off-shell Noether currents and potentials for the Holst Lagrangian generically depend on the Immirzi parameter, which holds even in the ‘half off-shell’and on-shell cases. We also study Killing vector fields in the ‘half off-shell’and on-shell cases. The current theoretical framework is illustrated for the ‘half off-shell’case in static spherically symmetric and Friedmann–Lemaitre–Robertson–Walker spacetimes in four dimensions. View Full-Text
Multidisciplinary Digital Publishing Institute
Publication date: 
1 Feb 2021

Merced Montesinos, Diego Gonzalez, Rodrigo Romero, Mariano Celada

Biblio References: 
Volume: 13 Issue: 2 Pages: 348