Conformally invariant averaged null energy condition from AdS/CFT

TL;DR

This paper derives a conformally invariant averaged null energy condition (CANEC) within the AdS/CFT framework, ensuring compatibility of bulk and boundary causality in curved spacetime boundaries.

Contribution

It generalizes the averaged null energy condition to curved boundaries in AdS/CFT, establishing a conformally invariant energy condition based on bulk-boundary causality principles.

Findings

Derived a conformally invariant averaged null energy condition (CANEC).

Linked bulk causality with boundary energy conditions.

Discussed implications for weak cosmic censorship.

Abstract

We study the compatibility of the AdS/CFT duality with the bulk and boundary causality, and derive a conformally invariant averaged null energy condition (CANEC) for quantum field theories in 3 and 5-dimensional curved boundaries. This is the generalization of the averaged null energy condition (ANEC) in Minkowski spacetime to curved boundaries, where null energy is averaged along the null line with appropriate weight for conformal invariance. For this purpose we take, as our guiding principle, the no-bulk-shortcut theorem of Gao and Wald, which essentially asserts that when going from one point to another on the boundary, one cannot take a "shortcut through the bulk". We also discuss the relationship between bulk vs boundary causality and the weak cosmic censorship.