For multi-black-hole axisymmetric initial data, either a multi-degenerate stationary vacuum spacetime exists, or m ≥ sqrt(|J|) with equality only for extreme Kerr.
Chru´ sciel,Mass and angular-momentum inequalities for axi-symmetric initial data sets
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The Mass-Angular Momentum Inequality for Multiple Black Holes
For multi-black-hole axisymmetric initial data, either a multi-degenerate stationary vacuum spacetime exists, or m ≥ sqrt(|J|) with equality only for extreme Kerr.