Midisuperspace laboratories for the dynamics of loop quantum gravity

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The study of how black holes evaporate is perhaps the most important outstanding problem in theoretical physics today. Its solution requires understanding the behavior of two of the pillars of modern physics, gravity and quantum field theory, in their most extreme regimes. Understanding how physical theories fit together in challenging regimes has in the past led to insights of spectacular consequences. An example of this could be Maxwell's understanding of how electricity and magnetism fit together, a synthesis that led to the discovery of radio waves, with the ensuing transformational changes they induced in our society. A second very important objective of this type of work is the formation of human resources of very high quality. Physicists trained in these disciplines have moved on to make contributions leading to rewarding careers in industry and in finance, as well as science.The group will study the application of techniques of loop quantum gravity in spherically symmetric contexts with the ultimate goal of understanding black hole evaporation. They will study the back-reaction of quantum fields living on spherically symmetric quantum space-times that they developed in a previous project. The discreteness of the quantum space-time naturally regularizes the infinities of quantum field theory yielding all results finite. To study the back reaction will require quantum space-times more realistic than the ones we have up to now, including dynamical evolution. They propose to find the quantum space-time of a collapsing shell and compute the back reaction of fields living on it. In addition to this they propose studying the structure of the quantum space-times we have up to now, in particular their singularity structure in the case of extremal and super extremal charged black holes and the Cauchy horizons that appear in the solutions. They also propose to continue the study of uniform discretizations as a quantization approach, in particular comparing with the exact quantization that was used to construct the spherical quantum space-times, which relied on the Abelianization of the algebra of constraints, a condition that one does not expect to generalize for more complex models. They will also explore a proposal for the problem of time and an ensuing proposal for solving the measurement problem in quantum mechanics. They wish to explore more general models than the ones worked out up to now and to study the issue of strong emergence.