# Geometric Analysis and Topology Seminar

#### The Impossibility of Periodic Motion in General Relativity

**Speaker:**
Spyros Alexakis, Toronto

**Location:**
Warren Weaver Hall 517

**Date:**
Friday, April 3, 2015, 11 a.m.

**Synopsis:**

The problem of motion of bodies in general relativity dates back to the early days of the theory. Initially considered in the slow-motion approximation, the derivation of the equations of motion to first post-Newtonian order is due to Einstein, Infeld and Hoffman, with much more precise approximations obtained since. A natural question considered in this connection is whether there exist solutions which are periodic in time--the problem of eternal return. For asymptotically simple space-times, we show that this is not possible, at least near infinity. We relate this to the problem of reconstructing a solution of the Einstein equations from knowledge of the radiation it has emitted towards infinity. Joint work with V. Schlue, and (partly) A. Shao.