In classical General Relativity, the values of fields on spacetime are uniquely determined by their values at an initial time within the domain of dependence of this initial data surface. However, it may occur that the spacetime under consideration extends beyond this domain of dependence, and fields, therefore, are not entirely determined by their initial data. This occurs, for example, in the well-known (maximally) extended Reissner-Nordstrom or Reissner-Nordstrom-deSitter (RNdS) spacetimes. The boundary of the region determined by the initial data is called the "Cauchy horizon." It is located inside the black hole in these spacetimes. The strong cosmic censorship conjecture asserts that the Cauchy horizon does not, in fact, exist in practice because the slightest perturbation (of the metric itself or the matter fields) will become singular there in a sufficiently catastrophic way that solutions cannot be extended beyond the Cauchy horizon. Thus, if strong cosmic censorship holds, the Cauchy horizon will be converted into a "final singularity," and determinism will hold. Recently, however, it has been found that, classically this is not the case in RNdS spacetimes in a certain range of mass, charge, and cosmological constant. In this paper, we consider a quantum scalar field in RNdS spacetime and show that quantum theory comes to the rescue of strong cosmic censorship. We find that for any state that is nonsingular (i.e., Hadamard) within the domain of dependence, the expected stress-tensor blows up with affine parameter, $V$, along a radial null geodesic transverse to the Cauchy horizon as $T_{VV} \sim C/V^2$ with $C$ independent of the state and $C \neq 0$ generically in RNdS spacetimes. This divergence is stronger than in the classical theory and should be sufficient to convert the Cauchy horizon into a strong curvature singularity.

中文翻译：

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Reissner-Nordström-deSitter 时空中柯西视界的量子不稳定性

在经典广义相对论中，时空场的值由它们在该初始数据表面的依赖域内的初始时间的值唯一确定。然而，所考虑的时空可能会超出这个依赖域，因此域并不完全由它们的初始数据决定。例如，这发生在众所周知的（最大）扩展的 Reissner-Nordstrom 或 Reissner-Nordstrom-deSitter (RNdS) 时空中。由初始数据确定的区域边界称为“柯西视界”。它位于这些时空的黑洞内。强大的宇宙审查猜想断言，柯西视界实际上并不 在实践中存在是因为（度量本身或物质场的）最轻微的扰动将以一种足够灾难性的方式变得奇异，以至于解决方案无法扩展到柯西视界之外。因此，如果强大的宇宙审查成立，柯西视界将转化为“最终奇点”，而决定论将成立。然而，最近发现，在一定的质量、电荷和宇宙常数范围内，RNdS 时空的经典情况并非如此。在本文中，我们考虑了 RNdS 时空中的量子标量场，并表明量子理论可以拯救强大的宇宙审查。我们发现，对于依赖域内的任何非奇异状态（即，Hadamard），预期应力张量随着仿射参数 $V$ 而爆炸，沿着横向于柯西视界的径向零测地线为 $T_{VV} \sim C/V^2$，其中 $C$ 独立于状态，$C \neq 0$ 一般在 RNdS 时空。这种发散比经典理论中的强，应该足以将柯西视界转换为强曲率奇点。