Abstract
In this short note, we prove that if an axially symmetric, asymptotically flat, stationary solution of the Einstein Vacuum Equation admits an involution interchanging the components of the event horizons, then the force between at least two of the event horizons must be positive. The proof is based on an observation that in this case the force can be expressed as a line integral with positive integrand.
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Li, Y.Y., Tian, G. Nonexistence of axially symmetric, stationary solution of Einstein Vacuum Equation with disconnected symmetric event horizon. Manuscripta Math 73, 83–89 (1991). https://doi.org/10.1007/BF02567630
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DOI: https://doi.org/10.1007/BF02567630