发表机构
Carnegie Mellon University; Cimulate, Salesforce（卡内基梅隆大学; Cimulate, Salesforce）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
利用点粒子有效场论精确计算旋转黑洞周围超轻矢量场的超辐射不稳定性速率，无需可分性假设，解决了文献中速率差异问题，并揭示了视界接触项的关键作用。
AI 中文摘要
我们使用点粒子有效场论来研究缓慢旋转黑洞周围超轻质量矢量的超辐射不稳定性速率。早期的有效理论处理报告了与在固定黑洞背景上求解Proca方程所得速率存在明显的$O(1)$差异，例如对于$j=1$和$\ell=2$的模式。我们表明实际上不存在差异：一旦正确识别简并$\{\ell=0,\ell=2\}$子空间中的领头阶态，有效理论（此处通过精确积分出引力子实现，并仅在之后按$\alpha$展开）就能精确重现所有$j=1$ Proca不稳定性速率，而且无需借助完整理论计算所依赖的FKKS ansatz。由于它从不依赖可分性，同样的方法至少在原则上适用于缺乏该ansatz所基于的隐藏对称性的旋转背景和天体。远区之外的唯一额外要素是一个保守的世界线接触项，即宇称偶$j=1$ Proca扇区中视界的静态单极响应，我们通过与近区匹配来确定该项。同一项将束缚态的精细结构劈移入与已发表的Proca谱精确一致。除了提供概念上直观的矢量超辐射模型并解决文献中明显的张力外，我们展示这项工作还旨在说明点粒子有效理论中涉及耗散效应的潜在技术微妙之处。
英文摘要
We use a point-particle effective field theory to study the superradiant instability rates of an ultralight massive vector around a slowly rotating black hole. Earlier effective-theory treatments reported an apparent $O(1)$ discrepancy with the rates obtained by solving the Proca equation on a fixed black-hole background, e.g. for the mode with $j=1$ and $\ell=2$. We show that there is in fact no discrepancy: once the leading-order states in the degenerate $\{\ell=0,\ell=2\}$ subspace are correctly identified, the effective theory (implemented here with the graviton integrated out exactly, and expanded in $α$ only afterwards) reproduces \emph{all} of the $j=1$ Proca instability rates exactly, and it does so \emph{without} ever invoking the FKKS ansatz on which the full-theory calculation rests. Since it never relies on separability, the same approach applies, at least in principle, to rotating backgrounds and bodies that lack the hidden symmetries underlying that ansatz. The single ingredient beyond the far zone is a conservative worldline contact term, the static monopole response of the horizon in the parity-even $j=1$ Proca sector, which we fix by matching to the near zone. The same term shifts the fine-structure splitting of the bound states into exact agreement with the published Proca spectrum. In addition to providing a conceptually straightforward model of vector superradiance and resolving an apparent tension in the literature, we present this work to illustrate potential technical subtleties involving dissipative effects in point particle effective theories.
Comments60 pages, 1 figure
