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arxiv: 1410.0665 · v2 · pith:LOGSXMPZnew · submitted 2014-10-02 · 🌀 gr-qc · math-ph· math.MP· quant-ph

Quantum inequality in spacetimes with small curvature

classification 🌀 gr-qc math-phmath.MPquant-ph
keywords quantuminequalitiescurvatureenergyfieldinequalityriccismall
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Quantum inequalities bound the extent to which weighted time averages of the renormalized energy density of a quantum field can be negative. They have mostly been proved in flat spacetime, but we need curved-spacetime inequalities to disprove the existence of exotic phenomena, such as closed timelike curves. In this work we derive such an inequality for a minimally-coupled scalar field on a geodesic in a spacetime with small curvature, working to first order in the Ricci tensor and its derivatives. Since only the Ricci tensor enters, there are no first-order corrections to the flat-space quantum inequalities on paths which do not encounter any matter or energy.

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