arXiv 2511.129022025-11-17gr-qchep-thmath-phmath.MP

修正引力与正则黑洞模型

Modified Gravity and Regular Black Hole Models

University of Alberta（阿尔伯塔大学）

Jose Pinedo Soto

备注：: PhD thesis, University of Alberta, Supervisor: Professor Valeri P. Frolov. 173 pages, 20 figures

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AI总结：

本文针对广义相对论存在时空奇点的理论缺陷，研究可消解奇点的修正引力理论，构建物理自洽的正则黑洞模型，验证了这类模型的可行性，为黑洞半经典描述提供新路径。

摘要：

时空奇点是曲率无穷大、经典物理失效的区域，对这类奇点的预测是广义相对论（GR）面临的最具深度的挑战之一。具体而言，施瓦西度规、克尔度规等黑洞解都存在中心奇点，这表明该理论在高曲率区间存在不完备性。本学位论文致力于研究修正引力理论，这类理论旨在消解上述奇点，构建物理上自洽的正则黑洞模型：这类黑洞保留事件视界，但全时空任意位置都不存在曲率发散问题。全文研究过程中，研究者特别注意确保所提出的模型具备物理合理性：模型可在合适的极限下退化为广义相对论，且能给出性质良好的曲率标量。这些研究结果共同证明了修正引力理论中正则黑洞模型的可行性，为构建自洽的黑洞半经典描述提供了极具潜力的路径，无需依赖量子引力来消解奇点。（完整摘要见原文档）

英文摘要：

The prediction of spacetime singularities, regions of infinite curvature where classical physics breaks down, is one of the most profound challenges in General Relativity (GR). In particular, black hole solutions such as the Schwarzschild and Kerr metrics feature central singularities that signal the incompleteness of the theory in high curvature regimes. This thesis is devoted to the study of modified theories of gravity that aim to resolve these singularities and construct physically viable models of regular black holes: black holes that retain an event horizon but exhibit no curvature divergence anywhere in the spacetime ... Throughout the thesis, particular care is taken to ensure that the proposed models are physically sensible: they reduce to GR in the appropriate limits and lead to well behaved curvature scalars. Collectively, these results highlight the viability of regular black hole models in modified gravity theories, providing a promising path toward a consistent semiclassical description of black holes that avoids the need for quantum gravitational resolution of singularities. (Full abstract can be found in document).

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