Quantum Effects for Black Holes and Analog Black Holes and the Validity of the Semiclassical Approximation

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Phenomena relating to microscopic (quantum) effects which occur during and after the formation of a black hole will be studied. The results will test predictions made using simple models in which the black hole exists in one space dimension and may provide insight into the important question of what happens to the information about how a black hole forms. If a system of very cold atoms called a Bose-Einstein condensate has its properties configured correctly, then quantum effects will occur which are in some important ways similar to those which occur for black holes. The difference is that Bose-Einstein condensates can be studied in the laboratory. An investigation of such systems will be made with the goal of making predictions for effects that could be observed in the laboratory. The validity of an important approximation called the semiclassical approximation that is used as a bridge between macroscopic (classical) and microscopic (quantum) phenomena will be studied in two cases. One is the effect of particle production on the dynamics of the universe for an important model in which the universe begins by contracting and later expands. The other is for the effect of particle production on a strong electric field. One or more graduate students and probably some undergraduates will participate in some aspects of the research, continuing a long history of their training in numerical and analytical research techniques and co-authorship on publications. The research proposed will investigate questions related to the information about how a black hole forms; the existence of quantum effects in analog black hole systems related to the existence of a horizon, which can be observed in laboratory studies; and the validity of the semi-classical approximation in certain cases where quantum effects are significant. In the case of black hole evaporation the objectives include determining the importance of quantum effects in the interior of a black hole and investigating the details of particle production in the exterior region during gravitational collapse to form a black hole, in order to gain insight into the question of what happens to the information about how a black hole forms and to check the accuracy of similar calculations in two dimensional dilaton theories of gravity. For Bose-Einstein condensates, which can serve as analogs for black holes, the goal is to determine whether undulations or other new observable effects that require the existence of a horizon are predicted to occur. The validity of the semiclassical approximation will be studied for one important model (de Sitter space) in which the contraction is to a minimum size and is followed by an expansion. Numerical computations of the stress-energy of quantum fields will be made in the black hole and cosmological investigations and in the cosmological case the backreaction on the spacetime geometry will be computed.