Two charged black holes in equilibrium

There is a quite instructive paper G. A. Alekseev and V. A. Belinski, Equilibrium configurations of two charged masses in General Relativity, Phys.Rev. D76 (2007) 021501; arXiv:0706.1981 [gr-qc], e.g. they mentioned a work about non-existence of static equilibrium configurations of two charged black holes by P. Chrusciel and P.Tod, Commun.Math.Phys., 271 577 (2007); arXiv:gr-qc/0512043 and found condition for equilibrium of two charged masses: $m_1 m_2 = (e_1-\gamma)(e_2+\gamma)$ with $\gamma = (m_2 e_1-m_1e_2)/(l+m_1+m_2)$.