The Golden Ratio Family of Extremal Kerr-Newman Black Holes and Its Implications for the Cosmological Constant

This work explores the geometry of extremal Kerr-Newman black holes by analyzing their mass/energy relationships and the conditions ensuring black hole existence. Using differential geometry in E3, we examine the topology of the event horizon surface and identify two distinct families of extremal black holes, each defined by unique proportionalities between their core parameters: mass (m), charge (Q), angular momentum (L), and the irreducible mass (mir). In the first family, these parameters are proportionally related to the irreducible mass by irrational numbers, with a characteristic flat Gaussian curvature at the poles. In the second family, we uncover a more intriguing structure where m, Q, and L are connected to mir through coefficients involving the golden ratio −ϕ−. Within this family lies a unique black hole whose physical parameters converge on the golden ratio, including the irreducible mass and polar Gauss curvature. This black hole represents the highest symmetry achievable within the constraints of the Kerr-Newman metric. This remarkable symmetry invites further speculation about its implications, such as the potential determination of the dark energy density parameter ΩΛ for Kerr-Newman-de Sitter black holes. Additionally, we compute the maximum energy that can be extracted through reversible transformations. We have determined that the second, golden-ratio-linked family allows for a greater energy yield than the first.