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The semiclassical backreaction equations are solved in closed RobertsonWalker spacetimes containing a positive cosmological constant and a conformally coupled massive scalar field. Renormalization of the stressenergy tensor results in higher derivative terms that can lead to solutions that vary on much shorter time scales than the solutions that would occur if the higher derivative terms were not present. These extra solutions can be eliminated through the use of order reduction. Four different methods of order reduction are investigated. These are first applied to the case when only conformally invariant fields, with and without classical radiation, are present. Then they are applied to the massive conformally coupled scalar field. The effects of different adiabatic vacuum states for the massive field are considered. It is found that if enough particles are produced, then the Universe collapses to a final singularity. Otherwise it undergoes a bounce, but at a smaller value of the scale factor (for the models considered) than occurs for the classical de Sitter solution. The stressenergy tensor incorporates both particle production and vacuum polarization effects. An analysis of the energy density of the massive field is done to determine when the contribution from the particles dominates.more » « lessFree, publiclyaccessible full text available November 1, 2024

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 Schwarzschildâ€“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

Vereshchagin, G. ; Ruffini, R. (Ed.)The symmetric twopoint function for a massless, minimally coupled scalar field in the Unruh state is examined for Schwarzschildde Sitter spacetime in two dimensions. This function grows linearly in terms of a time coordinate that is welldefined 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 twopoint function in two dimensions for a massive scalar field in Schwarzschildde Sitter spacetime is discussed.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

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