Faculty Research Perspectives
Naked, Hairy, Well-posed and Uncensored: Quantum Probing of Singular Spacetimes
Shadi Tahvildar-ZadehFebruary 25, 3:30 PM in Hill 705
Abstract.
To a physicist, the classical way of probing a singularity of a spacetime, is to throw a test particle at it and watch what happens. Classical particles have well-defined paths: they move along geodesics of spacetime. It is perhaps not surprising then that quantum probing involves the study of the well-posedness o f the wave equation on a given spacetime. Like all things quantum, this is tric ky business, in particular if the singularity in question is naked, i.e. can be seen from afar. Cosmic censorship is an attempt to banish naked singularities from the universe, claiming in effect that "if it can be seen, it doesn't exist." But who's afraid of naked singularities, you might ask? Suffice it to say that certain renowned cosmologists are known to have bet --and lost-- their shirt on this issue. In this talk, after providing the necessary background on Einstein's theory of gravitation, we consider a simple model of a spherically symmetric spacetime with an eternal naked singularity, and study the propagation of scala r waves on it, finding sufficient conditions for the well-posedness of the Cauchy problem, and obtaining certain a-priori estimates for the solutions, which also give us some evidence against the censorship conjectures. Along the way, we'll learn how to measure the hairiness of a naked singularity.
Warning: For mature audiences only. Contains explicit formulas involving humong ous integers.