Black Holes and Quantum Cosmology

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I propose to continue research in theoretical physics, primarily gravitational physics and cosmology, particularly focusing on the quantum aspects. One main focus is on quantum cosmology, applying quantum theory to the universe as a whole. One of the deepest problems in theoretical cosmology is the measure problem, how to obtain testable probabilities for observations by finite observers in a quantum model for the universe. Traditionally in quantum theory one uses what is called Born's rule, which says that probabilities are given by the squares of what in quantum theory are called amplitudes. However, I have discovered that Born's rule does not work in a universe large enough for there to be two observers so nearly identical that their observations do not distinguish them. I have proposed a new framework for converting quantum amplitudes to the probabilities of observations, but there are are unknown details. I would like to find better models for these details. A related issue in quantum cosmology is what is called the quantum state of the universe, which is a complete description of the universe in quantum theory, up to the question of how to determine observational probabilities from it. Hartle and Hawking have made the brilliant proposal of what they called the no-boundary wavefunction (NBWF). However, Susskind raised an objection to this model, which I fleshed out, that when empty space anti-gravitates, as it is observed to do in our universe (so that distant galaxies are accelerating apart), then the NBWF appears to be dominated by universes that are empty, obviously contrary to what we observe. Nevertheless, there is presently some controversy about how probabilities should be calculated in the NBWF, so I plan to examine this further to see whether it can be made consistent with observations, and, if not, what other proposals for the quantum state of the universe (and for the rules for getting the observational probabilities from the quantum state) could be consistent with observations. Another main focus of my continuing research is on black hole thermodynamics and Hawking evaporation, particularly for the information puzzle of what happens to the information that falls into a black hole. This puzzle was heightened by the argument of Almheiri, Marolf, Polchinski, and Sully, which suggests that black holes older than the so-called Page time are surrounded by what they call a `firewall,' which would immediately destroy anything falling in. I have written several papers critiquing this argument, and my graduate student Kento Osuga and I have built a toy model for getting the information out. I plan to work on improvements of this toy model. Smaller projects that I plan to pursue include better approximations for the geometry of an evaporating black hole, the time evolution and minimum temperature of a black hole of enormous electric charge, and the probabilities for the production of electron-positron pairs by colliding laser beams.