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–Nordström or Reissner–Nordström–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,
Twisted Self-Similarity and the Einstein Vacuum Equations
In the previous works [RSR19, SR22] we have introduced a new type of self-similarity for the Einstein
vacuum equations characterized by the fact that the homothetic vector field may be spacelike on the past
light cone of the singularity. In this work we give a systematic treatment of this new self-similarity. In
particular, we provide geometric characterizations of spacetimes admitting the new symmetry and show
the existence and uniqueness of formal expansions around the past null cone of the singularity which
may be considered analogues of the well-known Fefferman–Graham expansions. In combination with
results from [RSR19] our analysis will show that the twisted self-similar solutions are sufficiently general
to describe all possible asymptotic behaviors for spacetimes in the small data regime which are selfsimilar and whose homothetic vector field is everywhere spacelike on an initial spacelike hypersurface. We
present an application of this later fact to the understanding of the global structure of Fefferman–Graham
spacetimes and the naked singularities of [RSR19, SR22]. Lastly, we observe that by an amalgamation of
the techniques from [RSR18, RSR19], one may associate true solutions to the Einstein vacuum equations
to each of our formal expansions in a suitable region of spacetime.
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- Award ID(s):
- 1900288
- NSF-PAR ID:
- 10439473
- Date Published:
- Journal Name:
- Communications in mathematical physics
- ISSN:
- 1432-0916
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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