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Solution for Static, Spherically Symmetric Lovelock Gravity Coupled with Yang-Mills Hierarchy

The hierarchies of both Lovelock gravity and power-Yang-Mills field are combined through gravity in a single theory. In static, spherically symmetric ansatz exact particular integrals are obtained in all higher dimensions. The advantage of such hierarchies is the possibility of choosing coefficients, which are arbitrary otherwise, to cast solutions into tractable forms. To our knowledge the solutions constitute the most general spherically symmetric metrics that incorporate complexities both of Lovelock and Yang-Mills hierarchies within the common context. A large portion of our general class of solutions concern and addresses to black holes for which specific examples are given. Thermodynamical behaviors of the system is briefly discussed in particular dimensions.