On space-times with U(1) × U(1) symmetric compact Cauchy surfaces

Abstract

General space-times evolving from U(1) × U(1) symmetric Cauchy data prescribed on compact Cauchy surfaces are studied. Existence and properties of solutions of the constraint equations are analyzed. Some “canonical” forms of the metric are derived. When the spatial topology is S3 or S2 × S1 or L(p, q) we show that no singularities form before “the spacelike boundary of Gowdy's square” is reached.