Holographic reconstruction of asymptotically flat spacetimes

• URL: http://arxiv.org/abs/2203.15830v3
• Date: Mon, 23 May 2022 21:06:26 GMT
• Title: Holographic reconstruction of asymptotically flat spacetimes
• Authors: Erickson Tjoa and Finnian Gray
• Abstract summary: We present a "holographic" reconstruction of bulk spacetime geometry using correlation functions of a massless field living at the "future boundary" of the spacetime. 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 $mathcalM$ and those of another massless field living in three-dimensional null boundary $mathscrI+$.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $\mathscr{I}^+$.

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