This paper shows that a newly identified kind of symmetry of gravitational fields, called logarithmic supertranslations, is not only present at spatial infinity but also acts as a symmetry at null infinity. The authors give a direct derivation of these transformations at future null infinity, compute the associated conserved charges there, and check that those charges agree with the ones defined at spatial infinity at the “corner” where the two meet. Taken together, this completes the argument that the asymptotic symmetry group of asymptotically flat gravity contains these logarithmic supertranslations.

To give context, the familiar asymptotic symmetry group in flat spacetime is the Bondi–Metzner–Sachs (BMS) group. BMS includes ordinary translations and an infinite family of angle-dependent translations called supertranslations. Earlier work showed that one can consistently relax the standard boundary conditions at spatial infinity and get an enlarged algebra that includes extra transformations called logarithmic supertranslations. These were already linked to known infrared features of gravity, like a boundary “Goldstone mode” associated with breaking of supertranslation symmetry.

What the authors do here is bring that extension explicitly to null infinity, the region where outgoing radiation is observed. To do so they relax one of the usual technical gauge conditions used in the Bondi framework. Concretely, they allow certain metric components to contain terms that fall off with inverse powers of the radial coordinate r together with logarithmic dependence in r. Examples given include a relaxed form of g_rr (the radial-radial metric component) with 1/r^3 and logarithmic pieces, and corresponding log terms in the expansions of other metric functions such as those denoted B, V, and U^A. They keep other standard conditions (for instance certain determinant and angular components) but let the weaker, logarithmically corrected form accommodate the new symmetry generators. The vector fields that generate logarithmic supertranslations behave differently in r than ordinary supertranslations, and the paper notes an analogy with similar logarithmic gauge transformations known from electromagnetism.