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 “$t-{\varphi }^i$”-symmetric data which evaluates to the Arnowitt-Deser-Misner mass. We then show that $\mathbb{R}\times \mathrm{U}(1{)}^2$-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.

• Received 13 November 2014

DOI:https://doi.org/10.1103/PhysRevD.90.124078