DATA AT THE MOMENT OF INFINITE EXPANSION FOR

Abstract. In a recent paper by Thomas Jurke, it was proved that the asymp-totic behaviour of a solution to the polarized Gowdy equation in the expanding direction is of the form α ln t+β+ t−1/2ν+O(t−3/2), where α and β are con-stants and ν is a solution to the standard wave equation with zero mean value. Furthermore, it was proved that α, β and ν uniquely determine the solution. Here we wish to point out that given α, β and ν with the above properties, one can construct a solution to the polarized Gowdy equation with the above asymptotics. In other words, we show that α, β and ν constitute data at the moment of infinite expansion. We then use this fact to make the observation that there are polarized Gowdy spacetimes such that in the areal time coordi-nate, the quotient of the maximum and the minimum of the mean curvature on a constant time hypersurface is unbounded as time tends to infinity. 1