Averaged null energy condition and quantum inequalities in curved spacetime.
Abstract: The Averaged Null Energy Condition (ANEC) states that the integral
along a complete null geodesic of the projection of the stress-energy tensor onto the
tangent vector to the geodesic cannot be negative. ANEC can be used to rule out spacetimes
with exotic phenomena, such as closed timelike curves, superluminal travel and wormholes.
We prove that ANEC is obeyed by a minimally-coupled,... read morefree quantum scalar field on any
achronal null geodesic (not two points can be connected with a timelike curve) surrounded
by a tubular neighborhood whose curvature is produced by a classical source. To prove ANEC
we use a null-projected quantum inequality, which provides constraints on how negative the
weighted average of the renormalized stress energy tensor of a quantum field can be.
Starting with a general result of Fewster and Smith, we first derive a timelike projected
quantum inequality for a minimally-coupled scalar field on flat spacetime with a background
potential. Using that result we proceed to find the bound of a quantum inequality on a
geodesic in a spacetime with small curvature, working to first order in the Ricci tensor
and its derivatives. The last step is to derive a bound for the null-projected quantum
inequality on a general timelike path. Finally we use that result to prove achronal ANEC in
spacetimes with small curvature.
Thesis (Ph.D.)--Tufts University, 2015.
Submitted to the Dept. of Physics.
Advisor: Kenneth Olum.
Committee: Lawrence Ford, Alexander Vilenkin, Krzysztof Sliwa, and Mark Hertzberg.
Keyword: Physics.read less