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تسجيل مستخدم جديدQuantum stress tensor at the Cauchy horizon of Reissner-Nordstrom-deSitter spacetime
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The strong cosmic censorship conjecture proposes that starting from generic initial data on some Cauchy surface, the solutions of the Einstein equation should not be extendable across the boundary of the domain of dependence of that surface. For the case of the Reissner-Nordstrom-de Sitter spacetime this means that any perturbation should blow up sufficiently badly when approaching this boundary, called the Cauchy horizon. However, recent results indicate that for highly charged black holes classical scalar perturbations allow for a violation of strong cosmic censorship. In a recent paper arXiv:1912.06047, two of us have argued that quantum effects will restore censorship for generic values of the black hole parameters. But, due to practical limitations, the precise form of the divergence was only calculated for a small number of parameters. Here we perform a thorough parameter scan using an alternative, more efficient semi-analytic method. Our analysis confirms arXiv:1912.06047 in the sense that the quantum stress tensor is found to diverge badly generically. However, the sign of the divergence can be changed by changing the mass of the field or the spacetime parameters, leading to a drastically different type of singularity on the Cauchy horizon.
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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 e
xtends 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-Nordstrom or Reissner-Nordstrom-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 as $T_{VV} sim C/V^2$ with $C$ independent of the state and $C eq 0$ 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.
Despite of over thirty years of research of the black hole thermodynamics our understanding of the possible role played by the inner horizons of Reissner-Nordstrom and Kerr-Newman black holes in black hole thermodynamics is still somewhat incomplete:
There are derivations which imply that the temperature of the inner horizon is negative and it is not quite clear what this means. Motivated by this problem we perform a detailed analysis of the radiation emitted by the inner horizon of the Reissner-Nordstrom black hole. As a result we find that in a maximally extended Reissner-Nordstrom spacetime virtual particle-antiparticle pairs are created at the inner horizon of the Reissner-Nordstrom black hole such that real particles with positive energy and temperature are emitted towards the singularity from the inner horizon and, as a consequence, antiparticles with negative energy are radiated away from the singularity through the inner horizon. We show that these antiparticles will come out from the white hole horizon in the maximally extended Reissner-Nordstrom spacetime, at least when the hole is near extremality. The energy spectrum of the antiparticles leads to a positive temperature for the white hole horizon. In other words, our analysis predicts that in addition to the radiation effects of black hole horizons, also the white hole horizon radiates. The black hole radiation is caused by the quantum effects at the outer horizon, whereas the white hole radiation is caused by the quantum effects at the inner horizon of the Reissner-Nordstrom black hole.
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