Compact-axis conjecture for charged symmetric black holes

Consider ${\rm S}^{1}$-symmetric black holes whose fixed-point set, called the axis, is compact, and suppose the black hole has ends at which its charge is nonzero. Compact-axis black-hole conjecture. There are no ${\rm S}^{1}$-symmetric black holes with compact axis and having nonzero charge at each of their ends. The statement is a broader black-hole formulation related to the paper's preceding nonexistence conjectures for charged solutions on compact-axis and MKN-type configurations.