Boundary imprint of bulk causality

TL;DR

This paper explores how bulk causality in holographic spacetimes manifests on the boundary through hyperbolic surfaces, providing a Hamilton-Jacobi framework and deriving bulk geodesic equations from boundary properties.

Contribution

It introduces a Hamilton-Jacobi approach to boundary imprints of bulk lightcones and links bulk causality to boundary inclusion properties, advancing understanding of holographic correspondence.

Findings

Boundary hyperboloids encode bulk conformal metric.

Bulk causality implies boundary inclusion relations.

Bulk geodesic equations can be derived from boundary conditions.

Abstract

Motivated by the holographic correspondence, we study the boundary imprint of bulk lightcones in spacetimes with boundaries. These lightcones can be observed whenever a localized event takes place in the bulk. The associated boundary surfaces (hyperboloids) reveal the bulk conformal metric. We work out a Hamilton-Jacobi description of these surfaces and analyze them in explicit examples. Bulk causality translates into a boundary inclusion property from which the bulk geodesic equation can be derived under some assumptions.