Quantum field theory constrains traversable wormhole geometries
Abstract
Recently a bound on negative energy densities in fourdimensional Minkowski spacetime was derived for a minimally coupled, quantized, massless, scalar field in an arbitrary quantum state. The bound has the form of an uncertaintyprincipletype constraint on the magnitude and duration of the negative energy density seen by a timelike geodesic observer. When spacetime is curved and/or has boundaries, we argue that the bound should hold in regions small compared to the minimum local characteristic radius of curvature or the distance to any boundaries, since spacetime can be considered approximately Minkowski on these scales. We apply the bound to the stressenergy of static traversable wormhole spacetimes. Our analysis implies that either the wormhole must be only a little larger than Planck size or that there is a large discrepancy in the length scales which characterize the wormhole. In the latter case, the negative energy must typically be concentrated in a thin band many orders of magnitude smaller than the throat size. These results would seem to make the existence of macroscopic traversable wormholes very improbable.
 Publication:

Physical Review D
 Pub Date:
 May 1996
 DOI:
 10.1103/PhysRevD.53.5496
 arXiv:
 arXiv:grqc/9510071
 Bibcode:
 1996PhRvD..53.5496F
 Keywords:

 04.20.Gz;
 04.62.+v;
 Spacetime topology causal structure spinor structure;
 Quantum field theory in curved spacetime;
 General Relativity and Quantum Cosmology
 EPrint:
 26 pages, plain LaTex