In classical general relativity, the values of elds 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 elds,
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 elds) will become singular there in a sufciently 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 ‘nal 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 eld in RNdS spacetime
and show that quantum theory comes to the rescue of strong cosmic censorship.
We nd that for any state that is nonsingular (i.e., Hadamard) within the domain
of dependence, the expected stress-tensor blows up with afne parameter, V,
along a radial null geodesic transverse to the Cauchy horizon as TVV ∼ C/V
2 with C independent of the state and C 6= 0 generically in RNdS spacetimes.
This divergence is stronger than in the classical theory and should be sufcient
to convert the Cauchy horizon into a singularity through which the spacetime
cannot be extended as a (weak) solution of the semiclassical Einstein equation.
This behavior is expected to be quite general, although it is possible to have
C = 0 in certain special cases, such as the BTZ black hole
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:85005 |
| Date | 27 April 2023 |
| Creators | Hollands, Stefan, Wald, Robert M., Zahn, Jochen |
| Publisher | IOP Publishing |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, doc-type:article, info:eu-repo/semantics/article, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | 1361-6382, 115009 |
Page generated in 0.0014 seconds