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Abstract:  

The no-hair theorem states that the only asymptotically flat stationary solutions of the Einstein vacuum equations are members of the Kerr family, parametrized by mass and angular momentum. Hawking’s rigidity theorem shows that under the hypothesis of analyticity, any such solution is axially symmetric. For axially symmetric solutions with a single connected event horizon, Robinson (1975) proved that the solution must be Kerr. However, the case of multiple black holes has remained largely open. We settle this longstanding problem and show that stationary, axially symmetric multiple black holes cannot be in equilibrium by studying the associated harmonic maps with prescribed singularities. This is joint work with Qing Han, Marcus Khuri, and Jingang Xiong.