Determining an asymptotically AdS spacetime from data on its conformal boundary

TL;DR

This paper addresses how to reconstruct an asymptotically AdS spacetime satisfying Einstein's equations from boundary conformal data, advancing the understanding of the holographic principle in string theory.

Contribution

It provides a precise quantitative formulation of the real-time holographic principle for Einstein spacetimes and outlines its proof.

Findings

Establishes conditions for reconstructing Einstein metrics from boundary data

Provides a rigorous mathematical framework for the holographic prescription

Discusses physical implications of the holographic reconstruction

Abstract

An outstanding question lying at the core of the AdS/CFT correspondence in string theory is the holographic prescription problem for Einstein metrics, which asserts that one can slightly perturb the conformal geometry at infinity of the anti-de Sitter space and still obtain an asymptotically anti-de Sitter spacetime that satisfies the Einstein equations with a negative cosmological constant. The purpose of this paper is to address this question by providing a precise quantitative statement of the real-time holographic principle for Einstein spacetimes, to outline its proof and to discuss its physical implications.