Supertranslation in the bulk for generic spacetime

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 in arbitrary dimensions and unifies the realizations of supertranslations at null infinity and black hole horizons. The bulk supertranslation is connected to boundary supertranslation by characteristic flows. The associated symmetry algebra can be realized by light-ray operators defined on the null hypersurface. 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 in arbitrary dimensions and in four-dimensional Schwarzschild spacetime, where we uncover a novel curvature-induced memory effect with observable consequences for light propagation.