Abstract:

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

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