AI 中文总结
本论文针对广义相对论的三个开放性问题，从三个不同视角展开研究，推导了新的自对偶黑洞度规，提出了纽曼-贾尼斯算法的动力学探针对应形式，得到了无虚假极点的旋转黑洞康普顿振幅。
AI 中文摘要
广义相对论是一门已有百年历史的学科，但通过广义对称性、散射振幅和有效场论开展的现代探索提出了诸多开放性问题，促使人们重新评估关于引力、时空和自旋的传统观点。首先，在作为低能有效场论（EFT）的动力学引力中是否存在广义对称性？其次，是否存在场论层面的解释能说明广义相对论与杨-米尔斯理论之间的树级双拷贝关系？第三，在点粒子有效理论中，四维旋转黑洞在外场中的精确运动方程或拉格朗日量是什么？本论文从三个不同的引力视角展开研究，以阐明这些谜题。在第一部分，我们将引力视为洛伦兹群的规范理论，建立动力学引力的一形式对称性。在第二部分，我们结合色运动学对偶与双拷贝，探究引力可在多大程度上被视为微分同胚的规范理论。在第三部分，我们将四维引力视为自对偶与反自对偶部分之间的非线性相互作用，将这一视角应用于推导四维旋转黑洞解及其在点粒子有效理论中的动力学。首先，我们从经典双拷贝推导出一种新的自对偶黑洞度规，并证明克尔度规对应一对自对偶与反自对偶的陶布-努特（Taub-NUT）解，从而将纽曼-贾尼斯（Newman-Janis）算法提升为一种严格推导方法。其次，我们提出纽曼-贾尼斯算法的动力学探针对应形式，给出旋转黑洞康普顿振幅的拉格朗日推导，该振幅对所有螺旋度构型均表现出正确的因式分解且无虚假极点，同时构建了一种手征形式，以显现并最大化利用自对偶部分的简洁性。
英文摘要
General relativity is a century-old subject. Yet modern explorations through generalized symmetries, scattering amplitudes, and effective field theory have raised open problems, motivating a reassessment of conventional views on gravitation, spacetime, and spin. First, do generalized symmetries exist in dynamical gravity as a low-energy EFT? Second, is there a field-theoretic explanation for the tree-level double copy relationship between general relativity and Yang-Mills theory? Third, what are the exact equations of motion or Lagrangians of four-dimensional spinning black holes in external fields, in point-particle effective theory? In this dissertation, three different perspectives on gravity are developed to shed light on each of these puzzles. In Part I, we view gravity as a gauge theory of Lorentz group to establish a one-form symmetry of dynamical gravity. In Part II, we investigate how far gravity can be viewed as a gauge theory of diffeomorphisms, in connection with color-kinematics duality and double copy. In Part III, we view four-dimensional gravity as a nonlinear interaction between self-dual and anti-self-dual parts. We apply this view to the derivation of four-dimensional spinning black hole solutions as well as their dynamics in point-particle effective theory. First, we derive a new self-dual black hole metric from classical double copy and show that the Kerr metric represents a pair of self-dual and anti-self-dual Taub-NUT solutions, elevating the Newman-Janis algorithm to a rigorous derivation. Second, we propose a dynamical probe counterpart of Newman-Janis algorithm. We give a Lagrangian derivation of spinning black hole Compton amplitudes that exhibit correct factorizations and are free of spurious poles for all helicity configurations while developing a chiral formalism that manifests and maximally utilizes the simplicity of the self-dual sector.
Comments479 pages, 47 figures; Ph.D. thesis defended June 29, 2026. 14 Chapters: Introduction; Reimagining Gravity; Generalized Symmetries; Diffeomorphism Gauge Theories; Self-Dual BH from Double Copy; Newman-Janis from Taub-NUT Instantons; All-Orders Geodesic Deviation; Probe Newman-Janis Algorithm; Kerr & Kerr-Newman Effective Actions; Spinspacetime; Spinning BH EoM; Root-Kerr & Kerr Compton Amplitudes
