Holographic reconstruction of asymptotically 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 $\mathscr{I}^+$.