A gauge-invariant symplectic potential for tetrad general relativity

• DOI: 10.1007/jhep07(2018)040
• Publication Date: 2018-07-07T01:59:35Z
• Authors: Elena De Paoli; Simone Speziale
• Keywords: High Energy Physics - Theory; Black Holes; [PHYS.GRQC] Physics [physics]/General Relativity and Quantum Cosmology [gr-qc]; Space-Time Symmetries; mathematical methods; torsion; FOS: Physical sciences; QC770-798; General Relativity and Quantum Cosmology (gr-qc); 01 natural sciences; General Relativity and Quantum Cosmology; High Energy Physics - Theory (hep-th); tetrad; Nuclear and particle physics. Atomic energy. Radioactivity; Gauge Symmetry; 0103 physical sciences; general relativity; invariance: gauge; [PHYS.HTHE] Physics [physics]/High Energy Physics - Theory [hep-th]; potential: symplectic; Classical Theories of Gravity

Abstract

We identify a symplectic potential for general relativity in tetrad and connection variables that is fully gauge-invariant, using the freedom to add surface terms. When torsion vanishes, it does not lead to surface charges associated with the internal Lorentz transformations, and reduces exactly to the symplectic potential given by the Einstein-Hilbert action. In particular, it reproduces the Komar form when the variation is a Li derivative, and the geometric expression in terms of extrinsic curvature and 2d corner data for a general variation. The additional surface term vanishes at spatial infinity for asymptotically flat spacetimes, thus the usual Poincaré charges are obtained. We prove that the first law of black hole mechanics follows from the Noether identity associated with the covariant Lie derivative, and that it is independent of the ambiguities in the symplectic potential provided one takes into account the presence of non-trivial Lorentz charges that these ambiguities can introduce.