Upper and Lower Bounds on the Integrated Null Energy in Gravity

TL;DR

This paper establishes bounds on the integrated null energy in gravity using AdS/CFT, linking causality assumptions to energy constraints and verifying these bounds in wormhole models.

Contribution

It proves new lower and upper bounds on integrated null energy along achronal geodesics based on causality principles in AdS/CFT and gravitational settings.

Findings

Lower bound matches a recent conjecture for semiclassical gravity

Upper bound derived from achronality constraints

Bounds are satisfied in traversable wormhole constructions

Abstract

We prove a lower bound on the integrated null energy along achronal geodesic segments using induced gravity on a brane in AdS/CFT. The bound follows from the assumption that bulk causality respects brane causality, and matches a bound recently conjectured by Freivogel and Krommydas for semiclassical gravity. We also prove a more general upper bound on the same quantity that follows simply from achronality. We check that the lower bound is satisfied in recent constructions of traversable wormholes, and demonstrate that the bound is related to causality in the ambient spacetime of the wormhole.