黑洞时空中的重整化动力学摩擦
Renormalized Dynamical Friction in Black-Hole Spacetimes
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中文总结 AI 辅助
本文推导了黑洞时空中致密天体受引力自力的重整化局部运动方程，通过Schwinger--Keldysh轮廓积分环境与度规扰动，处理领头阶对数紫外发散，并给出适用于数值计算的完整重整化方案。
中文摘要 AI 辅助
我们推导了致密天体在黑洞时空中穿过物质运动时所受引力自力的重整化局部运动方程。我们在Schwinger--Keldysh轮廓上对环境和度规扰动进行积分，得到一个因果有效作用量，该作用量由按质量比和环境密度幂次组织的弯曲时空费曼图之和给出。在领头阶，环境尾流对世界线产生引力反作用。相应的图包含一个对数紫外发散，该发散重整化了领头阶耗散性流体-粒子耦合。我们通过局域大动量展开来分离该发散，在此展开中，弯曲时空推迟格林函数约化为其平坦切空间形式。我们将所得奇点转化为Barack--Ori模求和方案，推导出理想流体环境的解析穿刺和正则化参数。模相减固定了发散部分，但未固定有限的Wilson系数。对于无碰撞尘埃，我们通过将黑洞在介质中运动的精确近区计算进行匹配来确定该系数。这给出了一个适用于数值自力求计算的完整重整化方案。
英文摘要
We derive the renormalized local equation of motion for the gravitational self-force on a compact object moving through matter in a black-hole spacetime. We integrate out the environment and metric perturbations on a Schwinger--Keldysh contour, obtaining a causal effective action given by a sum of curved-spacetime Feynman diagrams organized by powers of the mass ratio and environmental density. At leading order, an environmental wake gravitationally backreacts on the worldline. The corresponding diagram contains a logarithmic ultraviolet divergence that renormalizes the leading dissipative fluid--particle coupling. We isolate the divergence with a local large-momentum expansion, in which the curved-spacetime retarded Green's function reduces to its flat tangent-space form. We translate the resulting singularity into a Barack--Ori mode-sum scheme, deriving an analytic puncture and regularization parameters for an ideal-fluid environment. Mode subtraction fixes the divergent part but not the finite Wilson coefficient. For collisionless dust, we determine this coefficient by matching to an exact near-zone calculation for a black hole moving through the medium. This gives a complete renormalization prescription suitable for numerical self-force calculations.
发表机构
- Carnegie Mellon University（卡内基梅隆大学）
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