Averaged null energy condition in spacetimes with boundaries
Abstract
The averaged null energy condition (ANEC) requires that the average along a complete null geodesic of the projection of the stressenergy tensor onto the geodesic tangent vector can never be negative. It is sufficient to rule out many exotic phenomena in general relativity. Subject to certain conditions, we show that the ANEC can never be violated by a quantized minimally coupled free scalar field along a complete null geodesic surrounded by a tubular neighborhood in which the geometry is flat and whose intrinsic causal structure coincides with that induced from the full spacetime. In particular, the ANEC holds in flat space with boundaries, as in the Casimir effect, for geodesics which stay a finite distance away from the boundary.
 Authors:
 Department of Mathematics, University of York, Heslington, York, YO10 5DD (United Kingdom)
 (United States)
 Publication Date:
 OSTI Identifier:
 21010920
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevD.75.025007; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CASIMIR EFFECT; COSMOLOGY; DISTANCE; GENERAL RELATIVITY THEORY; GEODESICS; GEOMETRY; SCALAR FIELDS; SPACETIME; VECTORS
Citation Formats
Fewster, Christopher J., Olum, Ken D., Pfenning, Michael J., Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, Massachusetts 02155, and Department of Physics, United States Military Academy, West Point, New York 10996. Averaged null energy condition in spacetimes with boundaries. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.025007.
Fewster, Christopher J., Olum, Ken D., Pfenning, Michael J., Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, Massachusetts 02155, & Department of Physics, United States Military Academy, West Point, New York 10996. Averaged null energy condition in spacetimes with boundaries. United States. doi:10.1103/PHYSREVD.75.025007.
Fewster, Christopher J., Olum, Ken D., Pfenning, Michael J., Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, Massachusetts 02155, and Department of Physics, United States Military Academy, West Point, New York 10996. Mon .
"Averaged null energy condition in spacetimes with boundaries". United States.
doi:10.1103/PHYSREVD.75.025007.
@article{osti_21010920,
title = {Averaged null energy condition in spacetimes with boundaries},
author = {Fewster, Christopher J. and Olum, Ken D. and Pfenning, Michael J. and Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, Massachusetts 02155 and Department of Physics, United States Military Academy, West Point, New York 10996},
abstractNote = {The averaged null energy condition (ANEC) requires that the average along a complete null geodesic of the projection of the stressenergy tensor onto the geodesic tangent vector can never be negative. It is sufficient to rule out many exotic phenomena in general relativity. Subject to certain conditions, we show that the ANEC can never be violated by a quantized minimally coupled free scalar field along a complete null geodesic surrounded by a tubular neighborhood in which the geometry is flat and whose intrinsic causal structure coincides with that induced from the full spacetime. In particular, the ANEC holds in flat space with boundaries, as in the Casimir effect, for geodesics which stay a finite distance away from the boundary.},
doi = {10.1103/PHYSREVD.75.025007},
journal = {Physical Review. D, Particles Fields},
number = 2,
volume = 75,
place = {United States},
year = {Mon Jan 15 00:00:00 EST 2007},
month = {Mon Jan 15 00:00:00 EST 2007}
}

We show, on fourdimensional Minkowski spacetime, that {l angle}{psi}{vert bar}{ital T}{sub {mu}{nu}}{vert bar}{psi}{r angle}, the renormalized expectation value in a general quantum state {vert bar}{psi}{r angle} of the stressenergy tensor for electromagnetism, satisfies the averagednullenergy condition, i.e., that {integral}{ital d}{lambda}{l angle}{psi}{vert bar}{ital T}{sub {mu}{nu}}{vert bar}{psi}{r angle}{ital t}{sup {mu}}{ital t{nu}}{ge}0 where this integral is along complete null geodesics with an affine parameter {lambda} and tangent vector {ital t}{sup {mu}}.

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