Quantum Instability of the Cauchy Horizon in ReissnerNordströmdeSitter Spacetime
Abstract
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 wellknown (maximally) extended ReissnerNordström or ReissnerNordströmdeSitter (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 stresstensor 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.
 Publication:

arXiv eprints
 Pub Date:
 December 2019
 DOI:
 10.48550/arXiv.1912.06047
 arXiv:
 arXiv:1912.06047
 Bibcode:
 2019arXiv191206047H
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 50 pages, abstract truncated due to arXiv length restriction. v2: minor corrections