Recovering the spacetime metric from a holographic dual

TL;DR

This paper reviews a method to reconstruct the bulk spacetime metric in holography using boundary light-cone cuts, extending it to black hole horizons and exploring conditions for the conformal factor.

Contribution

It introduces a novel approach to recover the bulk metric from boundary data, including near black hole horizons, and discusses conditions for determining the conformal factor.

Findings

Successful reconstruction of the conformal metric from boundary light-cone cuts

Extension of the method to black hole horizon regions

Conditions identified for determining the conformal factor

Abstract

We review our recent proposal to use certain spatial cross-sections of the boundary at infinity -- light-cone cuts -- to recover the conformal metric in the bulk. We discuss some extensions of this work, including how to obtain the conformal metric near the horizon of a collapsing black hole. We also show how to obtain the conformal factor under certain conditions.