Light-cone cuts and hole-ography: explicit reconstruction of bulk metrics

TL;DR

This paper combines light-cone cuts and hole-ography methods to explicitly reconstruct complete bulk metrics in locally AdS$_3$ spacetimes, overcoming individual limitations and enabling full metric recovery.

Contribution

It introduces a combined approach that overcomes limitations of each method, allowing complete bulk metric reconstruction in certain holographic theories.

Findings

Successfully reconstructed pure AdS$_3$, AdS$_3$ soliton, and BTZ black hole geometries.

Identified light-cone cuts via entanglement entropy.

Demonstrated the combined method overcomes individual limitations.

Abstract

In this paper, the two reconstruction methods, light-cone cuts method and hole-ography, are combined to provide complete bulk metrics of locally AdS$_3$ static spacetimes. As examples, our method is applied to the geometries of pure AdS$_3$, AdS$_3$ soliton, and BTZ black hole, and we see them successfully reconstructed. The light-cone cuts method is known to have difficulty in obtaining conformal factors, while the hole-ography in describing temporal components. Combining the two methods, we overcome the disadvantages and give complete metrics for a class of holographic theories such that entanglement wedge and causal wedge coincide. Light-cone cuts are identified by entanglement entropy in our method. We expect our study to lead to the discovery of a universal relation between the two methods, by which the combination would be applied to more generic cases.