DIFFERENTIAL GEOMETRY/PDE SEMINAR

Thursday, November 13, 2003 Padelford C-36 1:30 pm

Dynamics at singularities in General Relativity

Marsha Weaver (UW)

Appropriate initial data for Einstein’s equations determine a maximal Cauchy development. Even a geodesically complete initial data surface generally determines a maximal Cauchy development which is singular in the sense of geodesic incompleteness. Examples of inequivalent extensions of a such a maximal Cauchy development are known. Penrose conjectured more than 30 years ago that this nonuniqueness is exceptional.

A fruitful approach for confirming Penrose’s conjecture in various classes of solutions to Einstein’s equation is to understand the dynamics at the singularity well enough to show inextendibility. Two types of singularities have been found, oscillatory and monotone. It would be a great simplification if in the most general classes of solutions the dynamics at the singularity reduced to one of these two types.

In this talk, after introducing the above topics, I will describe a method which has been used to construct large classes of solutions with a monotone singularity, and discuss the current status of showing that oscillatory behavior occurs in large classes of solutions.

For more information about this seminar, visit the DG/PDE Seminar Web page (from the Math Department home page, www.math.washington.edu, follow the link Seminars, Colloquia, and Conferences).

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