Bulk supertranslation memories: a concept reshaping the vacua and black holes of general relativity

Abstract

The memory effect is a prediction of general relativity on the same footing as the existence of gravitational waves. The memory effect is understood at future null infinity as a transition induced by null radiation from a Poincaré vacuum to another vacuum. Those are related by a supertranslation, which is a fundamental symmetry of asymptotically flat spacetimes. In this essay, I argue that finite supertranslation diffeomorphisms should be extended into the bulk spacetime consistently with canonical charge conservation. It then leads to fascinating geometrical features of gravitational Poincaré vacua. I then argue that in the process of black hole merger or gravitational collapse, dramatic but computable memory effects occur. They lead to a final stationary metric which qualitatively deviates from the Schwarzschild metric.

Figures (1)

• Figure 1: Isometric embedding of the supertranslation horizon in Euclidean space $(x_s,y_s,z_s)$. The supertranslation field $C$ is either the $l=2$ (left) or $l=3$ (right) $m=0$ spherical harmonic.