# Colloquium: John M. Lee

### Event Description:

Title: A two-body problem in general relativity.

Abstract: Einstein’s 4-dimensional field equations of general relativity can be viewed as a coupled nonlinear evolution equation for a time-dependent Riemannian metric and second fundamental form. Initial data for this equation consist of a Riemannian metric $g$ on $M$ together with a symmetric $2$-tensor field $K$ representing the second fundamental form. Unlike the linear wave equation, these initial data cannot be specified independently, but must satisfy a necessary condition (based on the Gauss and Codazzi equations) called the \emph{Einstein constraint equations}. A good approach to parametrizing the possible solutions to Einstein's equations is to try to parametrize solutions to the constraint equations. One class of solutions that are of great interest to physicists for modeling isolated systems is the \emph{asymptotically hyperboloidal} ones, which have conformal compactifications at future lightlike infinity. I will talk about recent work with Paul Allen, Jim Isenberg, and Iva Stavrov on gluing together two such solutions to create a new solution, which contains (slight perturbations of) the two original ones.

### Event Contact

**Contact Name: **Dimiter Vassilev