Quantum fields do not satisfy the pointwise energy conditions that are assumed in the original singularity theorems of Penrose and Hawking. Accordingly, semiclassical quantum gravity lies outside their scope. Although a number of singularity theorems have been derived under weakened energy conditions, none is directly derived from quantum field theory. Here, we employ a quantum energy inequality satisfied by the quantized minimally coupled linear scalar field to derive a singularity theorem valid in semiclassical gravity. By considering a toy cosmological model, we show that our result predicts timelike geodesic incompleteness on plausible timescales with reasonable conditions at a spacelike Cauchy surface.

中文翻译：

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半经典奇点定理

量子场不满足彭罗斯和霍金的原始奇点定理中假设的逐点能量条件。因此，半经典量子引力不在他们的范围之内。尽管在能量减弱的条件下推导出了许多奇点定理，但没有一个是直接从量子场论推导出来的。在这里，我们采用由量化的最小耦合线性标量场满足的量子能量不等式来推导在半经典引力中有效的奇点定理。通过考虑一个玩具宇宙学模型，我们表明我们的结果预测了类空间柯西表面在合理的时间尺度上的类时测地线的不完整性和合理的条件。