Singular Supertranslations and Chern-Simons Theory on the Black Hole Horizon
arXiv:2212.00170 · doi:10.1103/PhysRevD.107.085019
Abstract
We construct the standard and dual supertranslation charges on the future horizon of the Schwarzschild black hole, using the first-order formulation of gravity with the Holst action. The Dirac bracket algebra of standard and dual supertranslation charges is shown to exhibit a central term in the presence of singularities in the two-sphere function associated with supertranslation. We show that one can cancel this anomalous term and restore the asymptotic symmetry algebra by introducing a gravitational Chern-Simons theory on the horizon. This demonstrates that consistency of the asymptotic symmetry algebra requires a new structure on the horizon.
arXiv comment47 pages
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