A gauge-invariant symplectic potential for tetrad general relativity
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
DOI:
10.1007/jhep07(2018)040
Publication Date:
2018-07-07T01:59:35Z
AUTHORS (2)
ABSTRACT
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.
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