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–Nordstrm–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.

我们在非阿贝尔 Kaluza-Klein 理论的源和无扭转极限的情况下考虑了 (4 + 3) 维弯曲时空中的 Weyl-Yang 规范引力理论。包含新自旋电流项和通常四维能量-动量张量的场方程的显式形式是通过众所周知的降维程序获得的。在此限制下，当存在与圆形和压扁的三球体S ³分别包括在内。(anti-)dyonic 解具有与爱因斯坦-杨-米尔斯系统的 Reissner-Nordstrm-de Sitter 黑洞相似的性质。然而，在这种方法中自然会出现宇宙常数，它与常数翘曲函数以及三球半径有关。结果表明，不仅挤压参数ℓ表现为恒定电荷，而且它的符号可以决定解是动态/单极子还是反动态/反单极子。使用幂级数方法还表明，非常规翘曲函数的存在对于在所考虑的模型中寻找新的精确类 Schwarzschild 解是必不可少的。