RUI: Studies of Singularities

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The singularity theorems tell us that singularities form in a large class of spacetimes, including the physically relevant cases of the big bang and of the gravitational collapse of a star to form a black hole. However, these theorems tell us very little about the nature of the singularities. For example, we would like to know the entire class of incomplete observers, how the curvature behaves along their world lines and whether they can see the singularity before they hit it. Since we do not have the general solution of Einstein's equation in closed form, Prof. Garfinkle intends to use all the methods available for the study of singularities: (i) to find exact solutions and study their singularities; (ii) to prove theorems about the behavior of singular spacetimes or (iii) to perform a numerical study of spacetimes with singularities to address these issues. Numerical evolution of generic initial data for axisymmetric cosmologies will be used to study the approach to the singularity of spatially inhomogeneous models. He will examine nonsingular, stationary electrovac solutions in general relativity and in string theory. He will also explore Choptuik's numerical discovery of scaling behavior in the formation of a zero mass singularity from the collapse of a spherically scalar field using a gauge invariant null initial value formulation. Perhaps the most important problem in the study of singularities is cosmic censorship: the issue of whether singularities are hidden behind event horizons. Work by Shapiro and Teukolsky suggests that highly prolate objects can form naked singularities during gravitational collapse. As an alternative, he will start a numerical investigation of the collapse of highly prolate gravity waves to see whether a naked singularity forms.