Extracting the bulk metric from boundary information in asymptotically AdS spacetimes

TL;DR

This paper presents two simple, computationally efficient methods using boundary null geodesic endpoints to reconstruct the entire bulk metric in asymptotically AdS spacetimes, with analysis of their applicability and limitations.

Contribution

It introduces two novel methods for bulk metric recovery from boundary data in AdS spacetimes and compares their practical advantages and limitations.

Findings

Two methods effectively recover bulk metrics from boundary geodesic data.

One method offers computational advantages over the other.

Partial bulk metric recovery is possible when full methods fail.

Abstract

We use geodesic probes to recover the entire bulk metric in certain asymptotically AdS spacetimes. Given a spectrum of null geodesic endpoints on the boundary, we describe two remarkably simple methods for recovering the bulk information. After examining the issues which affect their application in practice, we highlight a significant advantage one has over the other from a computational point of view, and give some illustrative examples. We go on to consider spacetimes where the methods cannot be used to recover the complete bulk metric, and demonstrate how much information can be recovered in these cases.