Supertranslations and Superrotations at the Black Hole Horizon

In this talk, we study the asymptotic symmetries in the near-horizon region of extremal and non-extremal black holes. By prescribing a physically sensible set of boundary conditions at the horizon, we derive the algebra of asymptotic Killing vectors, which is shown to be infinite-dimensional; it includes two sets of supertranslations and two mutually commuting copies of the Virasoro algebra. We define the surface charges associated to these large diffeomorphisms and evaluate them for different stationary black hole solutions. We finally discuss the relationship between these horizon charges and the Bondi-Metzner-Sachs (BMS) ones by computing the memory effect produced at the black hole horizon by a gravitational shock wave sent from null infinity.
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Leinweber Center for Theoretical Physics,
Apr 5, 2018, 6:32 AM