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The double smeared null energy condition

by Jackson R. Fliss, Ben Freivogel, Eleni-Alexandra Kontou

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Submission summary

Authors (as Contributors): Eleni-Alexandra Kontou
Submission information
Preprint link: scipost_202202_00025v2
Date accepted: 2022-06-28
Date submitted: 2022-06-02 18:06
Submitted by: Kontou, Eleni-Alexandra
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Gravitation, Cosmology and Astroparticle Physics
  • High-Energy Physics - Theory
Approach: Theoretical


The null energy condition (NEC), an important assumption of the Penrose singularity theorem, is violated by quantum fields. The natural generalization of the NEC in quantum field theory, the renormalized null energy averaged over a finite null segment, is known to be unbounded from below. Here, we propose an alternative, the double smeared null energy condition (DSNEC), stating that the null energy smeared over two null directions has a finite lower bound. We rigorously derive DSNEC from general worldvolume bounds for free quantum fields in Minkowski spacetime. Our method allows for future systematic inclusion of curvature corrections. As a further application of the techniques we develop, we prove additional lower bounds on the expectation values of various operators such as conserved higher spin currents. DSNEC provides a natural starting point for proving singularity theorems in semi-classical gravity.

Published as SciPost Phys. 14, 024 (2023)

List of changes

-Introduction: Added a sentence about the physical meaning of QEIs.

-Introduction: A reference on relative entropy was added.

-Section 2: Included more details on the renormalization procedure.

-Section 2: Explained the circle operator and the ultra regular domain.

-Section 2: The connection between the normal ordered stress energy tensor and the renormalized stress energy tensor is explained more.

- Section 3: The difference between equations (27) and (30) is now more explicit. The point-splitting procedure has additional details.

-Section 4: More details have been added regarding the incorporation of curvature in the bound.

-Section 4: Eq.(121) is fixed as it included wrong signs which however do not affect the rest of the calculation.

-Discussion: A paragraph was added on the topic of proving the DSNEC for holographic QFTs.

- Appendix B: The SNEC bound that was proven is now written explicitly.

-General: Typos were fixed throughout the manuscript.

Reports on this Submission

Anonymous Report 1 on 2022-6-5 (Invited Report)


The authors have properly addressed all of the points raised previously, and therefore, I highly recommend this paper to be published.

  • validity: high
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

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