Holographic reconstruction of asymptotically flat spacetimes

TL;DR

This paper develops a holographic method to reconstruct the interior geometry of asymptotically flat spacetimes from correlation functions at future null infinity, enabling interior insights from boundary data.

Contribution

It introduces a novel holographic reconstruction technique linking bulk spacetime geometry to boundary correlation functions at null infinity.

Findings

Bulk metric reconstructed from boundary correlators.

Asymptotic observers can infer interior geometry.

Holographic correspondence established for flat spacetimes.

Abstract

We present a "holographic" reconstruction of bulk spacetime geometry using correlation functions of a massless field living at the "future boundary" of the spacetime, namely future null infinity $\mathscr{I}^+$. It is holographic in the sense that there exists a one-to-one correspondence between correlation functions of a massless field in four-dimensional spacetime $\mathcal{M}$ and those of another massless field living in three-dimensional null boundary $\mathscr{I}^+$. The idea is to first reconstruct the bulk metric $g_{\mu\nu}$ by "inverting" the bulk correlation functions and re-express the latter in terms of boundary correlators via the correspondence. This effectively allows asymptotic observers close to $\mathscr{I}^+$ to reconstruct the deep interior of the spacetime using only correlation functions localized near $\mathscr{I}^+$.