Black hole memory effect

Symmetries of asymptotically flat spacetimes, the so-called Bondi-Metzner-Sachs (BMS) symmetries, consist of a very rich set composed of supertranslations and superrotations that extend the Poincaré group to an infinite-dimensional group. After a review of BMS symmetries at null infinity, I will show that supertranslation and superrotation symmetries also naturally arise in the near-horizon region of extremal and non-extremal black holes and have non-vanishing conserved charges associated to them. I will then discuss the relationship between these horizon charges and the BMS ones by computing the memory effect produced at the black hole horizon by a gravitational shock wave sent from null infinity.