标题： Born-Infeld引力中的纯量引力子 显示英文标题

标题： Scalar geons in Born-Infeld gravity

摘要： 在Born-Infeld引力的背景下，探索了静态、球对称且自引力的标量场解的存在性。通过解析近似法与数值方法的结合，求解了自由标量场（无势项）的方程，验证了这些解在远离中心区域时能恢复广义相对论的预测，但在中心区域发现了重要的新效应。我们根据史瓦西半径与Born-Infeld理论相关长度尺度的比值，发现了两类不同的对象：质量较大的解具有虫洞结构，其喉部位于 $r\approx 2M$；而对于较轻的构型，拓扑结构是欧几里得的。这些解的总能量密度表现出孤立子轮廓，峰值偏离中心，在存在虫洞的情况下，峰值位于喉部。分析了所考虑的各种构型的测地线结构和曲率不变量。 显示英文摘要

摘要： The existence of static, spherically symmetric, self-gravitating scalar field solutions in the context of Born-Infeld gravity is explored. Upon a combination of analytical approximations and numerical methods, the equations for a free scalar field (without a potential term) are solved, verifying that the solutions recover the predictions of General Relativity far from the center but finding important new effects in the central regions. We find two classes of objects depending on the ratio between the Schwarzschild radius and a length scale associated to the Born-Infeld theory: massive solutions have a wormhole structure, with their throat at $r\approx 2M$, while for the lighter configurations the topology is Euclidean. The total energy density of these solutions exhibits a solitonic profile with a maximum peaked away from the center, and located at the throat whenever a wormhole exists. The geodesic structure and curvature invariants are analyzed for the various configurations considered.