A black hole solution of higher-dimensional Weyl–Yang–Kaluza–Klein theory

Abstract

We consider the Weyl–Yang gauge theory of gravitation in a (4 + 3)-dimensional curved space-time within the scenario of the non-Abelian Kaluza–Klein theory for the source and torsion-free limits. The explicit forms of the field equations containing a new spin current term and the energy–momentum tensors in the usual four dimensions are obtained through the well-known dimensional reduction procedure. In this limit, these field equations admit (anti-)dyon and magnetic (anti-)monopole solutions as well as non-Einsteinian solutions in the presence of a generalized Wu–Yang ansatz and some specific warping functions when the extra dimensions associated with the round and squashed three-sphere S 3 are, respectively, included. The (anti-)dyonic solution has similar properties to those of the Reissner–Nordström–de Sitter black holes of the Einstein–Yang–Mills system. However, the cosmological constant naturally appears in this approach, and it associates with the constant warping function as well as the three-sphere radius. It is demonstrated that not only the squashing parameter ℓ behaves as the constant charge but also its sign can determine whether the solution is a dyon/monopole or an antidyon/antimonopole. It is also shown by using the power series method that the existence of nonconstant warping function is essential for finding new exact Schwarzschild-like solutions in the considered model.