Stability Within T^2-Symmetric Expanding Spacetimes

Abstract

We prove a nonpolarised analogue of the asymptotic characterisation of T^2-symmetric Einstein flow solutions completed recently by LeFloch and Smulevici. In this work, we impose a condition weaker than polarisation and so our result applies to a larger class. We obtain similar rates of decay for the normalised energy and associated quantities for this class. We describe numerical simulations which indicate that there is a locally attractive set for T^2-symmetric solutions not covered by our main theorem. This local attractor is distinct from the local attractor in our main theorem, thereby indicating that the polarised asymptotics are unstable.