Delving into the heart of theoretical physics, this paper unveils a general relation for the total angular momentum of regular solutions within the framework of Einstein–Yang–Mills–Higgs equations. The study opens new avenues in understanding the dynamics of complex physical systems. By deriving this fundamental relationship, the research bridges different theoretical models. It focuses specifically on two intriguing physical configurations: rotating dyons and rotating magnetic dipoles, exploring their behavior as particular instances of the derived equation. The authors delve into the challenging realm of rotating pure Einstein–Yang–Mills regular solutions, further expanding the scope of their investigation. The analysis of these solutions provides valuable insights into the interplay between gravity and other fundamental forces. The study poses the absence of rotating regular solitons with a net magnetic charge based on the obtained results. This hypothesis significantly contributes to the ongoing discourse on the existence and properties of exotic topological solitons. These findings have profound implications for our understanding of fundamental physics. By exploring the angular momentum and properties of regular solutions, the research expands our knowledge of complex theoretical models, potentially stimulating further research into rotating dyons, magnetic dipoles, and other exotic phenomena. It contributes to the continuing refinement of our understanding of the universe's fundamental laws.
Published in the International Journal of Modern Physics A, a journal dedicated to high-energy physics, gravitation, and cosmology, this paper aligns perfectly with the journal’s scope. Its exploration of Einstein–Yang–Mills–Higgs equations and rotating solutions directly contributes to the journal’s ongoing coverage of theoretical developments in modern physics. The focus on angular momentum and magnetic charge fits well with the journal’s interest in fundamental physical phenomena.