The averaged null energy conditions in even dimensional curved spacetimes from AdS/CFT duality

Abstract

We consider averaged null energy conditions (ANEC) for strongly coupled quantum field theories in even (two and four) dimensional curved spacetimes by applying the no-bulk-shortcut principle in the context of the AdS/CFT duality. In the same context but in odd-dimensions, the present authors previously derived a conformally invariant averaged null energy condition (CANEC), which is a version of the ANEC with a certain weight function for conformal invariance. In even-dimensions, however, one has to deal with gravitational conformal anomalies, which make relevant formulas much more complicated than the odd-dimensional case. In two-dimensions, we derive the ANEC by applying the no-bulk-shortcut principle. In four-dimensions, we derive an inequality which essentially provides the lower-bound for the ANEC with a weight function. For this purpose, and also to get some geometric insights into gravitational conformal anomalies, we express the stress-energy formulas in terms of geometric quantities such as the expansions of boundary null geodesics and a quasi-local mass of the boundary geometry. We argue when the lowest bound is achieved and also discuss when the averaged value of the null energy can be negative, considering a simple example of a spatially compact universe with wormhole throat.

arXiv comment30 pages, two figures

References in corpus (17)

• The Black Hole in Three Dimensional Space Time
• Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence
• Gravitational Energy in Spherical Symmetry
• Does backreaction enforce the averaged null energy condition in semiclassical gravity?
• Theorems on gravitational time delay and related issues
• Dynamics in Non-Globally-Hyperbolic Static Spacetimes III: Anti-de Sitter Spacetime
• Averaged Null Energy Condition from Causality
• Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition
• Achronal averaged null energy condition
• A holographic proof of the averaged null energy condition
• Averaged null energy condition violation in a conformally flat spacetime
• Conformally invariant averaged null energy condition from AdS/CFT
• Achronal ANEC, Weak Cosmic Censorship, and AdS/CFT duality
• Global aspects of conformal symmetry and the ANEC in dS and AdS
• Bounds on the local energy density of holographic CFTs from bulk geometry
• Achronal averaged null energy condition for extremal horizons and (A)dS
• Vacuum energy is non-positive for (2+1)-dimensional holographic CFTs

Cited by in corpus (2)

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