标题： 弯曲时空中的负能量密度限制 显示英文标题

标题： Restrictions on negative energy density in a curved spacetime

摘要： 近期，Pfenning 和 Ford 对于最小耦合标量场，在“全局静态”（超静态）时空内静止观察者所测得的（重整化的）能量密度上提出了一个限制（“量子不等式型关系”），这是对Ford和Roman提出的平直时空量子不等式型关系的推广。他们发现了能量密度沿线积分乘以采样（加权）函数后的负下界，并对一些特定时空显式地进行了评估。 本文研究了类空超曲面是紧致且无边界的时空的下界问题。在短“采样时间”极限下，该界限具有渐近展开。尽管由于积分的非局域性，一般情况下此展开不能用局部不变量表示，但我们仍用不变量显式地计算出极限中的主要项。我们还估算了长采样时间极限下的界限。 显示英文摘要

摘要： Recently a restriction ("quantum inequality-type relation") on the (renormalized) energy density measured by a static observer in a "globally static" (ultrastatic) spacetime has been formulated by Pfenning and Ford for the minimally coupled scalar field, in the extension of quantum inequality-type relation on flat spacetime of Ford and Roman. They found negative lower bounds for the line integrals of energy density multiplied by a sampling (weighting) function, and explicitly evaluate them for some specific spacetimes. In this paper, we study the lower bound on spacetimes whose spacelike hypersurfaces are compact and without boundary. In the short "sampling time" limit, the bound has asymptotic expansion. Although the expansion can not be represented by locally invariant quantities in general due to the nonlocal nature of the integral, we explicitly evaluate the dominant terms in the limit in terms of the invariant quantities. We also make an estimate for the bound in the long sampling time limit.