Mass functional for initial data in 4+1-dimensional spacetime

We consider a broad class of asymptotically flat, maximal initial data sets satisfying the vacuum constraint equations, admitting two commuting rotational symmetries. We construct a mass functional for “t-ϕi”-symmetric data which evaluates to the Arnowitt-Deser-Misner mass. We then show that R×U(1)2-invariant solutions of the vacuum Einstein equations are critical points of this functional amongst this class of data. We demonstrate the positivity of this functional for a class of rod structures which include the Myers-Perry initial data. The construction is a natural extension of Dain’s mass functional to D=5, although several new features arise.