Stefan Hollands - Semi-classical analysis of strong cosmic censorship

This talk was part of the Thematic Programme on "Spectral Theory and Mathematical Relativity" held at the ESI June 5, 2023 — July 28, 2023. 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-Nordstr{\"o}m or Reissner-Nordstr{\"o}m-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, 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 provided the mass, charge, and cosmological constant are in a certain regime. In this talk, we consider a quantum scalar field in RNdS spacetime and show that quantum theory comes to the rescue of strong cosmic censorship. We show that for any state that is nonsingular (i.e., Hadamard) within the domain of dependence, the expected stress-tensor blows up as TVV ~C/V2, where V is an affine parameter along a radial null geodesic transverse to the Cauchy horizon. Unlike in classical theory, the strength of the singularity cannot be weakened by tuning the mass, charge or cosmological constant. This behavior is quite general, i.e., it generically holds for all spacetimes where the Cauchy horizon is a Killing horizon, although it is possible to have C=0 in certain special cases, such as the BTZ black hole. Joint work with C. Klein, R. M. Wald, J. Zahn