AI 中文总结
研究爱因斯坦-标量-高斯-博内引力中两类标量-高斯-博内耦合函数下的非阿贝尔单极子，通过分析耦合函数对单极子解分支结构的影响，揭示多项式耦合导致临界解及几何相变，指数耦合起调节作用，还探讨了临界解的物理解释。
AI 中文摘要
我们研究了爱因斯坦-标量-高斯-博内引力中两类标量-高斯-博内耦合函数下的静态、球对称自引力非阿贝尔 't Hooft-Polyakov 单极子。证明了单极子解的分支结构敏感地依赖于耦合函数的选择。对于多项式耦合，耦合参数足够大时，场方程主部在临界半径处局部退化，导致临界解，标志着几何相变。指数耦合则是自然调节器，防止主部退化并保持场分布平滑。最后讨论了临界解可能的物理解释，即时空分为量子引力效应可能重要的内部区域和经典广义相对论能很好描述的外部区域。
英文摘要
We study static, spherically symmetric self-gravitating non-Abelian 't Hooft-Polyakov monopoles in Einstein-scalar-Gauss-Bonnet gravity for two classes of scalar-Gauss-Bonnet coupling functions. We demonstrate that the branch structure of the monopole solutions depends sensitively on the choice of the coupling function. For the polynomial coupling, we show that, for sufficiently large values of the coupling parameter, the principal part of the field equations becomes locally degenerate at a critical radius, leading to a critical solution that signals a geometric phase transition. By contrast, the exponential coupling acts as a natural regulator, preventing the degeneration of the principal part and preserving smooth field profiles. Finally, we discuss a possible physical interpretation of the critical solution, in which spacetime separates into an inner region where quantum-gravitational effects may become important and an outer region that remains well described by classical general relativity.
Comments10 pages, 3 figures
