The Dynamics of Quantum Gravity: Symmetry Reduced Models

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We study the dynamics of canonical quantum gravity in a variety of 1+1 dimensional model systems including spherically symmetric gravity coupled to fields in four dimensions and the Callan-Giddings-Harvey-Strominger black holes. Among the techniques used are recently developed local gauge fixings, loop quantum gravity treatments, and a new paradigm for dealing with the dynamics of totally constrained theories that we have been developing over the last few years. The paradigm consists in constructing discrete theories such that the continuum theory of interest arises as a well defined limit. It has points in common with that of lattice gauge theory, where discrete theories are used in a limiting procedure to define a continuum theory of interest. This approach has already been applied successfully in some situations where the space-time has some spatial dependence (i.e. more complicated than homogeneous cosmologies) but without genuine degrees of freedom, most notably providing a characterization of the complete space-time of a non-singular loop quantum gravity black hole. We propose here to extend it to richer models with dependence on one spatial coordinate. The models include complex phenomena like the one discussed by Choptuik in gravitational collapse and at the quantum level can accommodate Hawking radiation. We also continue our investigation on the role of using physical clocks and rods in describing quantum mechanics, to apply high performance computing techniques to loop quantum cosmology and to explore astrophysical implications of loop quantum gravity effects in the evaporation of primordial black holes.This research fits within fundamental physics, the area of research that concerns itself with how the laws of physics fit together. In this case the laws of gravity that rule the large scales of the universe with the laws of quantum mechanics that describe the microscopic world. Sometimes by understanding how the laws of physics fit together remarkable insights can be achieved that lead to practical applications far beyond what anyone could have envisioned. Apart from the intrinsic research aspects, broader impacts of this proposal are aiding in the creation of human resources in US physics through the training of a postdoctoral researcher and the possibility that the techniques introduced here may have applicability in other areas of science and engineering as well. In addition to that, various outreach activities for the general public are planned that will help not only disseminate the results of this proposal but those of the community of physicists working on the subfield of loop quantum gravity as a whole.