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 ${\mathcal{I}}^{+}$. 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 ${\mathcal{I}}^{+}$. 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 ${\mathcal{I}}^{+}$ to reconstruct the deep interior of the spacetime using only correlation functions localized near ${\mathcal{I}}^{+}$.

arXiv comment10 pages, single column; Essay written for the Gravity Research Foundation 2022 Awards for Essays on Gravitation --- Honourable Mention. Submitted to IJMPD for consideration as part of GRF special issue. arXiv admin note: text overlap with arXiv:2204.13133

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