 Award ID(s):
 1912584
 NSFPAR ID:
 10443723
 Editor(s):
 Vereshchagin, G.; Ruffini, R.
 Date Published:
 Journal Name:
 Proceedings of the Sixteenth Marcel Grossmann Meeting on General Relativity
 Page Range / eLocation ID:
 1255 to 1264
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
More Like this

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 latetime behaviors of some of the modes of the quantum fields and of the symmetric twopoint 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 latetime limit when the radial coordinate is held fixed. The behavior of the symmetric twopoint 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.more » « less

A bstract Twodimensional Schwarzschildde Sitter is a convenient spacetime in which to study the effects of horizons on quantum fields since the spacetime contains two horizons, and the wave equation for a massless minimally coupled scalar field can be solved exactly. The twopoint correlation function of a massless scalar is computed in the Unruh state. It is found that the field correlations grow linearly in terms of a particular time coordinate that is good in the future development of the past horizons, and that the rate of growth is equal to the sum of the black hole plus cosmological surface gravities. This time dependence results from additive contributions of each horizon component of the past Cauchy surface that is used to define the state. The state becomes the BunchDavies vacuum in the cosmological far field limit. The two point function for the field velocities is also analyzed and a peak is found when one point is between the black hole and cosmological horizons and one point is outside the future cosmological horizon.more » « less

Vereshchagin, G. ; Ruffini, R. (Ed.)A method is presented which allows for the numerical computation of the stressenergy tensor for a quantized massless minimally coupled scalar field in the region outside the event horizon of a 4D Schwarzschild black hole that forms from the collapse of a null shell. This method involves taking the difference between the stressenergy tensor for the in state in the collapsing null shell spacetime and that for the Unruh state in Schwarzschild spacetime. The construction of the modes for the {\it in} vacuum state and the Unruh state is discussed. Applying the method, the renormalized stressenergy tensor in the 2D case has been computed numerically and shown to be in agreement with the known analytic solution. In 4D, the presence of an effective potential in the mode equation causes scattering effects that make the the construction of the in modes more complicated. The numerical computation of the in modes in this case is given.more » « less

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 wellknown (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 stresstensor blows up with affine parameter,
V , along a radial null geodesic transverse to the Cauchy horizon asT _{VV}∼C /V ^{2}withC independent 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. 
The static patch of de Sitter spacetime and the Rindler wedge of Minkowski spacetime are causal diamonds admitting a true Killing field, and they behave as thermodynamic equilibrium states under gravitational perturbations. We explore the extension of this gravitational thermodynamics to all causal diamonds in maximally symmetric spacetimes. Although such diamonds generally admit only a conformal Killing vector, that seems in all respects to be sufficient. We establish a Smarr formula for such diamonds and a ``first law" for variations to nearby solutions. The latter relates the variations of the bounding area, spatial volume of the maximal slice, cosmological constant, and matter Hamiltonian. The total Hamiltonian is the generator of evolution along the conformal Killing vector that preserves the diamond. To interpret the first law as a thermodynamic relation,it appears necessary to attribute a negative temperature to the diamond, as has been previously suggested for the special case of the static patch of de Sitter spacetime. With quantum corrections included, for small diamonds we recover the ``entanglement equilibrium'' result that the generalized entropy is stationary at the maximally symmetric vacuum at fixed volume, and we reformulate this as the stationarity of free conformal energy with the volume not fixed.more » « less