Semi-classical analysis of strong cosmic censorship

Stefan Hollands (U Leipzig)

Jul 14. 2023, 14:00 — 14:50

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 $T_{VV} \sim C/V^2$, 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

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Spectral Theory and Mathematical Relativity (Thematic Programme)
Piotr T. Chruściel (U of Vienna)
Peter Hintz (ETH Zurich)
Alexander Strohmaier (U Leeds)
Steven Morris Zelditch † (Northwestern U Evanston)