Numerical study of generic, expanding T²-Symmetric vacuum spacetimes

Generic expanding T²-Symmetric vacuum spacetimes can be described by a metric which contains two gravitational-wave polarizations propagating in a background spacetime. The metric depends only on one spatial variable and time. Additional off-diagonal metric components yield a non-zero “twist”. Evolving spacetimes of maximal genericity are characterized by non-zero constants of the motion A and B defined as spatial integrals of nonlinear combinations of the metric variables and their first derivatives. Studies of subclasses of these spacetimes with non-zero twist and B = 0 have yielded theorems describing the asymptotics in the limit of infinite expansion. However, rigorous results do not exist for the B ≠ 0 case. Instead, in [1], numerical simulations are used to determine the asymptotics including finding the correct asymptotic power law, demonstrating the existence of attractors in the dynamics, and discovering the interchange of energy between the two gravitational-wave polarizations. The current focus will be on remaining open questions and possible ways to address them.

[1] B.K. Berger, J. Isenberg, A. Layne, Phys. Rev. D 108, 104015 (2023)