Journal of High Energy Physics

, 2019:133 | Cite as

Upper and lower bounds on the integrated null energy in gravity

  • Stefan Leichenauer
  • Adam LevineEmail author
Open Access
Regular Article - Theoretical Physics


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.


AdS-CFT Correspondence Classical Theories of Gravity 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of Physics, Alphabet (Google) XMountain ViewU.S.A.
  2. 2.Department of PhysicsUniversity of CaliforniaBerkeleyU.S.A.
  3. 3.Kavli Institute for Theoretical PhysicsUniversity of CaliforniaSanta BarbaraU.S.A.

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