# Quantum Instability of the Cauchy Horizon in Reissner-NordstrÃ¶m-deSitter Spacetime

December 12, 2019

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\"om or Reissner-Nordstr\"om-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.

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