Unified holographic constructions at spatial and timelike infinity

Construct analogous holographic boundary stress tensors and holographic dictionaries for three-dimensional asymptotically flat spacetimes at spatial infinity and future and past timelike infinity, extending the null-infinity construction and establishing a unified treatment of all asymptotic regions.

Background

The paper constructs a quasilocal holographic stress tensor and associated dictionary at future null infinity for three-dimensional asymptotically flat spacetimes. The conformal boundary also contains spatial infinity and future and past timelike infinity, whose asymptotic geometries differ from the Carrollian geometry at null infinity. Because the asymptotic regions are linked by matching conditions and conserved charges, a unified treatment would extend the holographic description to the complete boundary of the scattering spacetime.

References

We believe a similar construction exists for AFS$_3$ as well. In this article, we construct the boundary stress tensor and holographic dictionary at null infinity, leaving the analogous constructions at spatial and timelike infinity for future work.

— Aspects of Carrollian field theory from holography  (2608.12241 - Krishna et al., 12 Aug 2026) in Section 1, Introduction and Summary of Results

For AFS, the bulk trace $T{a}_{a}\propto M(\phi)$ does not vanish. But we do not understand its connection with the Carrollian Weyl anomaly yet.

— Aspects of Carrollian field theory from holography  (2608.12241 - Krishna et al., 12 Aug 2026) in Section 3, Boundary theory and its central charges, subsection “The Carrollian stress tensor”