Abstract:

We show that extreme Myers–Perry initial data realize the unique absolute minimum of the total mass in a physically relevant (Brill) class of maximal, asymptotically flat, bi-axisymmetric initial data for the Einstein equations with fixed angular momenta. As a consequence, we prove the relevant mass-angular momentum inequality in this setting for 55-dimensional spacetimes. That is, all data in this class satisfy the inequality \(m^3\geq \frac{27\pi}{32}\left(|\mathcal{J}_1|+|\mathcal{J}_2|\right)^2\), where mm and \(\mathcal{J}_i, i=1,2,\) are the total mass and angular momenta of the spacetime. Moreover, equality holds if and only if the initial data set is isometric to the canonical slice of an extreme Myers–Perry black hole.

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