Quantum inequality in spacetimes with small curvature.

Quantum inequalities bound the extent to which weighted time averages of the renormalized energy density of a quantum field can be negative. Such inequalities in curved spacetime can be used to disprove the existence of exotic phenomena, such as closed timelike curves. Starting with a general result of Fewster and Smith, we derive a quantum 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 inequality on paths which do not encounter any matter or energy. [ABSTRACT FROM AUTHOR]