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

TL;DR

This paper derives higher-dimensional black hole solutions within Weyl-Yang-Kaluza-Klein theory, revealing how extra dimensions and warping functions influence dyonic and monopole configurations, and introduces new exact Schwarzschild-like solutions.

Contribution

It presents explicit higher-dimensional black hole solutions in Weyl-Yang-Kaluza-Klein theory, including the effects of warping functions and extra dimensions on dyonic and monopole solutions, with new Schwarzschild-like solutions.

Findings

Existence of (anti-)dyon and monopole solutions similar to Reissner-Nordström-de Sitter black holes.

Cosmological constant naturally emerges from the warping functions and extra dimensions.

Nonconstant warping functions are crucial for new Schwarzschild-like solutions.

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$-$Nordstr\"{o}m$-$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 $\ell$ 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.