AI 中文总结
本文通过双时标微扰展开研究克尔背景下黑洞视界的演化方程，推导粗粒化视界动力学约束，构建含能量等的黑洞守恒定律，为极端质量比旋近相关研究提供框架。
AI 中文摘要
黑洞事件视界遵循一组支配其内禀和外禀几何的演化方程。我们在克尔背景下对这些方程进行双时标微扰展开，推导粗粒化视界动力学的强约束。在主导阶，粗粒化线性剪切消失，视界呈现绝热刚性：其角速度和非亲和性的主导修正在每个视界截面上保持均匀，同时在慢时标上演化。随后，我们提供一套系统程序，将例如洛伦兹规范下的微扰体解转换为适配视界的向内纽曼-昂蒂规范，允许直接从体度量中提取微扰视界几何。最后，我们构建与视界对称性相关的黑洞守恒定律，包括能量、动力学熵和角动量。我们在微扰论中展开荷至二阶、通量至三阶，为未来应用于极端质量比旋近中的视界吸收和反作用提供框架。
英文摘要
Black-hole event horizons obey a set of evolution equations governing their intrinsic and extrinsic geometry. We study these equations in a \textit{two-timescale} perturbative expansion about a Kerr background and derive strong constraints on the coarse-grained horizon dynamics. At leading order, the coarse-grained linear shear vanishes, while the horizon exhibits an \textit{adiabatic rigidity}: the leading corrections to its angular velocity and inaffinity remain uniform on each horizon cut, while evolving on the slow timescale. We then provide a systematic procedure for transforming a perturbative bulk solution, given for example in Lorenz gauge, to an ingoing Newman--Unti gauge adapted to the horizon, allowing the perturbed horizon geometry to be extracted directly from the bulk metric. Finally, we formulate black-hole conservation laws associated with horizon symmetries, including energy, dynamical entropy, and angular momentum. We expand the charges through second order and their fluxes through third order in perturbation theory, providing a framework for future applications to horizon absorption and backreaction in extreme mass-ratio inspirals.
Comments33 pages, 1 figure
