Supertranslations in the bulk of spacetime

Abstract

Supertranslations are usually defined as asymptotic symmetries associated with spacetime boundaries, such as null infinity and black hole horizons. In this Letter, we show that supertranslations admit a natural, coordinate-independent extension into the bulk of spacetime, realized as transitions between families of null hypersurfaces. This construction applies to generic spacetimes admitting null boundaries with residual symmetries and unifies the realizations of supertranslations at null infinity and finite-distance null hypersurfaces such as black hole horizons. The bulk supertranslation is connected to boundary supertranslation by characteristic flows. The associated symmetry algebra at the linearized level can be realized by light-ray operators defined on the null hypersurface and the bulk supertranslation acts as a zero-mode operator in the context of light-cone quantization. Within this framework, the gravitational wave memory effect corresponds to a shift of null hypersurfaces in the bulk. As explicit examples, we compute bulk supertranslations in Minkowski spacetime and four-dimensional Schwarzschild spacetime, where we uncover a novel curvature-dependent memory effect with observable consequences for light propagation.