Mixmaster spacetime, Geroch’s transformation, and constants of motion
Mixmaster spacetime, Geroch’s transformation, and constants of motion
We show that for U(1)-symmetric spacetimes on ${\mathit{S}}^{3}$\ifmmode\times\else\texttimes\fi{}R a constant of motion associated with the well known Geroch transformation, a functional K[${\mathit{h}}_{\mathit{i}\mathit{j}}$,${\mathrm{\ensuremath{\pi}}}^{\mathit{i}\mathit{j}}$], quadratic in gravitational momenta, is strictly positive in an open subset of the set of all U(1)-symmetric initial data, and therefore not weakly zero. The mixmaster initial data …