A gauge-invariant symplectic potential for tetrad general relativity
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Publication:2413676
DOI10.1007/JHEP07(2018)040zbMATH Open1395.83046arXiv1804.09685WikidataQ129546800 ScholiaQ129546800MaRDI QIDQ2413676
Author name not available (Why is that?)
Publication date: 14 September 2018
Published in: (Search for Journal in Brave)
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 Lie 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 Poincare 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.
Full work available at URL: https://arxiv.org/abs/1804.09685
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