Studies Relating to Black Hole Evaporation and to the Validity of the Semiclassical Approximation in Cosmology

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This award supports studies on black hole evaporation processes, with a focus on investigating quantum effects during and after the formation of a black hole. The results may provide insight into the important question of what happens to the information about how a black hole forms. Bose-Einstein condensates are systems that typically contain very cold atoms. For certain configurations, quantum effects will occur which are in some important ways similar to those that occur for black holes. Experimental studies of Bose-Einstein condensate analog black holes have been carried out. Theoretical calculations will be made using the same techniques as are used to study quantum effects related to real black holes. The results will be compared with the experimental data. The semiclassical approximation has been used to investigate quantum effects such as particle production in a variety of situations including the early universe. It provides a bridge between macroscopic (classical) and microscopic (quantum) phenomena. It's validity will be studied for an important model in which the universe is initially contracting, reaches a minimum size, and then begins to expand. Particle production is expected to be particularly important during the contracting phase where it could significantly alter the dynamical evolution of the universe. The results will help to determine whether the semiclassical approximation is valid in cases where quantum effects are significant. Four 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. Results will be disseminated to the research community through publications and presentations at national and international meetings. Some results obtained will be relevant for condensed matter physics.The research supported by this grant addresses black hole evaporation, observable effects in Bose-Einstein condensates which can serve as black hole analogs, and early universe cosmology. Specifically, it will investigate questions related to the information about how a black hole forms, the correspondence between theoretical and experimental results related to quantum effects in analog black hole systems, and the validity of the semi-classical approximation in models of the universe. In the case of black hole evaporation, the objectives include studying in detail quantum effects that occur if a spherically symmetric null shell collapses to form a black hole. One goal is to check the accuracy of similar calculations in two dimensional dilaton theories of gravity. It is also possible that insight will be gained into the question of what happens to the information about how the black hole formed. Bose-Einstein condensates that can serve as analog black holes have been created in the laboratory. The goal is to determine whether certain experimental results are in quantitative agreement with predictions resulting from quantum field theory in curved space calculations in the analog spacetime. The primary goal for cosmology is to determine whether the semiclassical approximation is valid for models in which the universe contracts to a minimum size and then expands. The models used will consist of a closed universe with a positive cosmological constant. For the black hole evaporation project the stress-energy tensor for a quantized massless minimally coupled scalar field will be numerically computed in four-dimensions in the case of a null shell that collapses to form the black hole. For the cosmology project the semiclassical backreaction equations will be solved numerically in the case that a massive conformally coupled scalar field is present. The results will be used to investigate the validity of the semiclassical approximation in a collapsing universe. The density density correlation function for a Bose-Einstein condensate analog black hole will be computed using quantum field theory in curved space techniques for a model that closely matches the velocity and sound speed profiles used in the experiments.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.