General Relativity and Gravitation

, Volume 41, Issue 9, pp 2113–2130

Non-existence of stationary two-black-hole configurations


  • Gernot Neugebauer
    • Theoretisch-Physikalisches InstitutFriedrich-Schiller-Universität
    • Max-Planck-Institut für GravitationsphysikAlbert-Einstein-Institut

DOI: 10.1007/s10714-009-0840-8


We resume former discussions of the question, whether the spin–spin repulsion and the gravitational attraction of two aligned black holes can balance each other. To answer the question we formulate a boundary value problem for two separate (Killing-) horizons and apply the inverse (scattering) method to solve it. Making use of results of Manko, Ruiz and Sanabria-Gómez and a novel black hole criterion, we prove the non-existence of the equilibrium situation in question.


Inverse scattering method Spin-spin repulsion Double-Kerr-NUT solution Sub-extremal black holes


We would like to thank Marcus Ansorg and David Petroff for many valuable discussions. This work was supported by the Deutsche Forschungsgemeinschaft (DFG) through the Collaborative Research Centre SFB/TR7 “Gravitational wave astronomy”.

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© The Author(s) 2009