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

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-Nordstrom-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.

Automated summary

The study explores the Weyl-Yang gauge theory of gravitation in a (4 + 3)-dimensional curved space-time, focusing on field equations in the usual four dimensions and finding solutions like (anti-)dyons, magnetic (anti-)monopoles, and non-Einsteinian solutions. The presence of the cosmological constant and its association with warping functions and three-sphere radius are highlighted, along with the importance of nonconstant warping functions for discovering new exact Schwarzschild-like solutions.