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1. Linear growth of the two-point function for the Unruh state in 1 + 1 dimensional black holes

   https://doi.org/10.1142/9789811269776_0100  

   Anderson, Paul R.; Scofield, Zachary P.; Traschen, Jennie (January 2023, Proceedings of the Sixteenth Marcel Grossmann Meeting on General Relativity)

   Vereshchagin, G.; Ruffini, R. (Ed.)

   The symmetric two-point function for a massless, minimally coupled scalar field in the Unruh state is examined for Schwarzschild-de Sitter spacetime in two dimensions. This function grows linearly in terms of a time coordinate that is well-defined on the future black hole and cosmological horizons, when the points are split in the space direction. This type of behavior also occurs in two dimensions for other static black hole spacetimes when the field is in the Unruh state, and at late times it occurs in spacetimes where a black hole forms from the collapse of a null shell. The generalization to the case of the symmetric two-point function in two dimensions for a massive scalar field in Schwarzschild-de Sitter spacetime is discussed. 

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2. Infrared effects and the Unruh state

   https://doi.org/10.1088/1361-6382/acd0fd  

   Anderson, Paul R; Gholizadeh Siahmazgi, Shohreh; Scofield, Zachary P (May 2023, Classical and Quantum Gravity)

   Abstract Detailed behaviors of the modes of quantized scalar fields in the Unruh state for various eternal black holes in two dimensions are investigated. It is shown that the late-time behaviors of some of the modes of the quantum fields and of the symmetric two-point function are determined by infrared effects. The nature of these effects depends upon whether there is an effective potential in the mode equation and what form this potential takes. Here, three cases are considered, one with no potential and two with potentials that are nonnegative everywhere and are zero on the event horizon of the black hole and zero at either infinity or the cosmological horizon. Specifically, the potentials are a delta function potential and the potential that occurs for a massive scalar field in Schwarzschild–de Sitter spacetime. In both cases, scattering effects remove infrared divergences in the mode functions that would otherwise arise from the normalization process. When such infrared divergences are removed, it is found that the modes that are positive frequency with respect to the Kruskal time on the past black hole horizon approach zero in the limit that the radial coordinate is fixed and the time coordinate goes to infinity. In contrast, when there is no potential and thus infrared divergences occur, the same modes approach nonzero constant values in the late-time limit when the radial coordinate is held fixed. The behavior of the symmetric two-point function when the field is in the Unruh state is investigated for the case of a delta function potential in certain asymptotically flat black hole spacetimes in two dimensions. The removal of the infrared divergences in the mode functions results in the elimination of terms that grow linearly in time. 

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3. Encoding beyond cosmological horizons in de Sitter JT gravity

   https://doi.org/10.1007/JHEP02(2023)179  

   Levine, Adam; Shaghoulian, Edgar (February 2023, Journal of High Energy Physics)

   A bstract Black hole event horizons and cosmological event horizons share many properties, making it natural to ask whether our recent advances in understanding black holes generalize to cosmology. To this end, we discuss a paradox that occurs if observers can access what lies beyond their cosmological horizon in the same way that they can access what lies beyond a black hole horizon. In particular, distinct observers with distinct horizons may encode the same portion of spacetime, violating the no-cloning theorem of quantum mechanics. This paradox is due precisely to the observer-dependence of the cosmological horizon — the sharpest difference from a black hole horizon — although we will argue that the gravity path integral avoids the paradox in controlled examples. 

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4. Gravitational duals to the grand canonical ensemble abhor Cauchy horizons

   https://doi.org/10.1007/JHEP10(2020)102  

   Hartnoll, Sean A.; Horowitz, Gary T.; Kruthoff, Jorrit; Santos, Jorge E. (October 2020, Journal of High Energy Physics)

   null (Ed.)

   A bstract The gravitational dual to the grand canonical ensemble of a large N holographic theory is a charged black hole. These spacetimes — for example Reissner- Nordström-AdS — can have Cauchy horizons that render the classical gravitational dynamics of the black hole interior incomplete. We show that a (spatially uniform) deformation of the CFT by a neutral scalar operator generically leads to a black hole with no inner horizon. There is instead a spacelike Kasner singularity in the interior. For relevant deformations, Cauchy horizons never form. For certain irrelevant deformations, Cauchy horizons can exist at one specific temperature. We show that the scalar field triggers a rapid collapse of the Einstein-Rosen bridge at the would-be Cauchy horizon. Finally, we make some observations on the interior of charged dilatonic black holes where the Kasner exponent at the singularity exhibits an attractor mechanism in the low temperature limit. 

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5. Quantum instability of the Cauchy horizon in Reissner–Nordström–deSitter spacetime

   https://doi.org/10.1088/1361-6382/ab8052  

   Hollands, Stefan; Wald, Robert M.; Zahn, Jochen (May 2020, Classical and Quantum Gravity)

   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 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,V, along a radial null geodesic transverse to the Cauchy horizon asT_VV∼C/V²withCindependent of the state andC≠ 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 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 haveC= 0 in certain special cases, such as the BTZ black hole. 

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