Quantitative Force Bounds, Rod-Separation Geometry, and Komar-Spin Monotonicity in the Exact Symmetric Corotating Kerr–Newman Binary

We investigate quantitative force bounds and rod-separation properties of the known exact symmetric binary solution describing two identical, corotating Kerr–Newman black holes with equal electric charges and vanishing individual magnetic charges, held apart by a conical strut. The metric, interaction-force expression and interacting horizon half-length are established results from the existing literature. Our contribution is a detailed algebraic analysis of these exact expressions, subject to the positive-horizon-rod condition. We establish the global implication that positivity of the interacting horizon-rod quantity implies strict positivity of the force numerator throughout the finite-separation formal algebraic domain. The proof uses an exhaustive parameter decomposition, including the sector in which the isolated-body subextremality parameter is negative. On the nonnegative subextremality sector, we derive explicit lower bounds for the force numerator and the interaction force. We further establish a strict monotonicity result for the relation between the solution rotation parameter and the constituent Komar angular momentum on the outer subextremal separated branch. This gives a unique implicit conversion between the solution parameter and the physical angular momentum at fixed mass, charge and separation. A fixed-Komar-angular-momentum large-separation expansion is also derived and checked against the established asymptotic expansion of the exact solution. Additional results concern the algebraic relation between the strut-force factor and coordinate-rod separation, including the distinction between the outer attractive branch and inner formal repulsive configurations. An exact inner-domain counterexample demonstrates why the Komar-spin monotonicity result cannot be extended to the entire formal positive-rod domain. The analysis is deliberately restricted to the specified exact Kerr–Newman binary family. The formal algebraic positive-rod domain is distinguished from the globally regular electrovacuum spacetime class. No new exact metric, general black-hole uniqueness theorem or universal no-balance theorem is claimed. The manuscript includes explicit algebraic certificates and supplementary exact-arithmetic verification materials. AI assistance : This work was produced with substantial assistance from an AI system (ChatGPT, Claude, Gemini). The proofs have not yet been independently checked by a human specialist. Corrections are welcome.