Jackson R. Fliss, Ben Freivogel, Eleni-Alexandra Kontou
SciPost Phys. 14, 024 (2023) ·
published 27 February 2023
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.
Ben Freivogel, Eleni-Alexandra Kontou, Dimitrios Krommydas
SciPost Phys. 13, 001 (2022) ·
published 15 July 2022
The classic singularity theorems of General Relativity rely on energy
conditions that can be violated in semiclassical gravity. Here, we provide
motivation for an energy condition obeyed by semiclassical gravity: the smeared
null energy condition (SNEC), a proposed bound on the weighted average of the
null energy along a finite portion of a null geodesic. We then prove a
semiclassical singularity theorem using SNEC as an assumption. This theorem
extends the Penrose theorem to semiclassical gravity. We also apply our bound
to evaporating black holes and the traversable wormhole of
Maldacena-Milekhin-Popov, and comment on the relationship of our results to
other proposed semiclassical singularity theorems.
Dr Kontou: "We thank the referee for revie..."
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