Presented by: 
Todd Oliynyk (Monash University)
Date: 
Mon 15 Apr, 2:00 pm - 3:00 pm
Venue: 
Mansergh Shaw 45-204

The visible universe contains many different types of dynamical compact bodies including asteroids, comets, planets, stars and even more exotic objects such as neutron stars. In spite of their fundamental importance to astrophysics and cosmology, there are currently very few analytical results available that apply to these dynamical bodies. In particular, even the most basic problem of establishing the (local) existence and uniqueness of solutions that represent gravitating compact bodies was, until very recently, a long standing open problem in General Relativity (GR). In this talk, I will discuss this problem and pay particular attend to the case of elastic matter. After presenting some general background on the dynamics of compact bodies in GR, I will describe, in detail, the initial value formulation for the particular case of elastic matter and outline the analytic difficulties that have hindered progress in understand the initial value problem for this system. I will then summarize recent results obtained in collaboration with Lars Anderson and Bernd Schmidt in which we establish the existence and uniqueness of solutions that represent gravitating dynamical elastic bodies. Time permitting, I will describe some open problems and promising directions for future work.