Black hole memory effect

TL;DR

This paper analyzes the black hole memory effect caused by gravitational shockwaves, revealing horizon superrotations and supertranslations, and extends the analysis to charged black holes, connecting near-horizon symmetries with observable charges.

Contribution

It provides a near-horizon perspective on black hole memory effects, including superrotation and supertranslation charges, and extends the framework to Einstein-Maxwell and Reissner-Nordström black holes.

Findings

Horizon superrotation charges match BMS superrotation at infinity.

Supertranslation contributes to entropy change.

Extended analysis to Einstein-Maxwell and Reissner-Nordström black holes.

Abstract

We compute the memory effect produced at the black hole horizon by a transient gravitational shockwave. As shown by Hawking, Perry, and Strominger (HPS) such a gravitational wave produces a deformation of the black hole geometry which from future null infinity is seen as a Bondi-Metzner-Sachs (BMS) supertranslation. This results in a diffeomorphic but physically distinct geometry which differs from the original black hole by their charges at infinity. Here we give the complementary description of this physical process in the near-horizon region as seen by an observer hovering just outside the event horizon. From this perspective, in addition to a supertranslation the shockwave also induces a horizon superrotation. We compute the associated superrotation charge and show that its form agrees with the one obtained by HPS at infinity. In addition, there is a supertranslation contribution to the horizon charge, which measures the entropy change in the process. We then turn to electrically and magnetically charged black holes and generalize the near-horizon asymptotic symmetry analysis to Einstein-Maxwell theory. This reveals an additional infinite-dimensional current algebra that acts non-trivially on the horizon superrotations. Finally, we generalize the black hole memory effect to Reissner-Nordstr\"{o}m black holes.