Black Holes and Quantum Cosmology

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An overarching goal of theoretical physics is to find (1) the complete set of dynamical laws governing the evolution of the universe, (2) the quantum state as a particular solution of those dynamical laws, and (3) the rules for extracting observational probabilities from the quantum state. Hartle and Hawking have emphasized that just knowing the complete dynamical laws would not be enough to give a complete description of the universe without also knowing the actual solution of the dynamical laws (i.e., the quantum state). I have more recently emphasized that even knowing both the complete dynamical laws and the quantum state would still not be enough, as one also needs to know how to get the probabilities for the various possible observations from the quantum state. I have further shown that Born's rule for probabilities as expectation values of projection operators does not work for a large universe. I am proposing to continue and extend my research in all three of these key areas, as well as in more minor areas.In (1), I plan to look at the quantum gravity dynamics of black holes, which appears to require nonlocal features, going beyond quantum field theory. I plan to investigate how suitable nonlocality, perhaps along with what I have called Extreme Cosmic Censorship, may allow black hole formation and evaporation to preserve information and yet prevent the occurrence of firewalls that have been proposed to form just inside old black holes.In (2), I plan to look for classes of quantum states that would be both simple and also consistent with our observations. One such class appears to be those obeying my proposed Extreme Cosmic Censorship, which are quantum states that in the semiclassical limit have neither big bang nor big crunch singularities. I propose to investigate what a more precise quantum description of such states might be. In (3), I plan to look for rules that solve the measure problem of eternal inflationary cosmology, how to give well-defined probabilities for observations in universes that expand to become indefinitely large so that there appears to be infinitely many observations of many different types. In such cases, the ratios of the numbers of different types of observations become the ambiguous ratios of infinite numbers, so that a better prescription is needed for giving the probabilities. I have already proposed measures that seem to be statistically consistent with our observations, but none of them are so elegant as desired, so there is room for improvement. One seeks a complete theory for the dynamical laws, quantum state, and rules for extracting observational probabilities from it that is both as simple as possible and that gives as high a probability as possible for what we observe. These two requirements are generally somewhat at odds with each other, but one wants to make this product as large as possible. Therefore, finding the right trade-off between simplicity and likelihood is the challenge facing the formation of a complete theory of the universe.Other more minor problems for students, PDFs, and myself to study include ab initio estimates of constants of physics, integrability of the Einstein equations, the critical metric for two inspiralling massless particles, compact Einstein metrics on connected sums of the products of two 2-spheres, escaping the Solar System without emitting rocket exhaust, a comparison of Newtonian and general relativistic homogeneous anisotropic cosmologies, an isometric embedding of the horizon of the extreme Kerr horizon metric into 3-dimensional flat space, the two maxima and one minimum in between of the speed of a ball falling far enough through the atmosphere, and Schwinger pair production in focused colliding laser beam pulses.