Kerr--Newman Memory Effect

TL;DR

This work places Kerr–Newman black holes within the Bondi–Sachs framework to study gravitational memory from both null infinity and near-horizon perspectives. By transforming Kerr–Newman into Bondi–Sachs gauge via zero angular momentum geodesics, the authors compute the memory effects produced by a transient gravitational shock and relate them to BMS supertranslations and superrotations. They find that at null infinity the memory does not excite the pure supertranslation charge, but it alters the superrotation sector and leaves the zero-modes largely unchanged; in the near-horizon extremal limit, the memory induces horizon superrotations and implants soft electric hair through the electromagnetic field, with a nontrivial coupling between angular momentum and charge. These results reveal a distinct, observer-dependent structure of memory: null infinity and the horizon encode different aspects of the scattering, and the electromagnetic interaction can significantly modify horizon charges, suggesting higher-order analyses are needed to fully distinguish Kerr–Newman from Kerr in asymptotic data.

Abstract

We bring the Kerr--Newman spacetime into the Bondi--Sachs gauge by means of zero angular momentum, null geodesics. We compute the memory effect produced at the black hole horizon by a transient gravitational shock wave, which from future null infinity is seen as a Bondi-Metzner-Sachs supertranslation. This results in a change of the supertransformation charges at infinity between the spacetime geometries defined by the black hole before, and after, the shockwave scattering. For an extremal Kerr--Newman black hole, we give the complementary description of this process in the near-horizon limit, as seen by an observer hovering over the horizon. In this limit, we compute the supertranformation charges and compare them to those calculated at null infinity. We analyze the effect of these transformations on the electromagnetic gauge field and explore the self-interaction between this and the angular momentum of the black hole.