发表机构
Southern University of Science and Technology（南方科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该文提出一个模型无关框架，证明黑洞动力学 Love 数在任意静态球对称时空上普遍对数跑动，并推导出主递推公式，应用于 Reissner-Nordström 等黑洞，揭示其极端极限下跑动消失等关键性质。
AI 中文摘要
在广义相对论（GR）中，静态潮汐 Love 数为零，但在更一般的理论或超出静态极限的情况下，它们通常非零，并且实际上随尺度呈对数跑动。我们提出了一个与模型无关的框架，用于描述 Love 数在动力学层面的跑动，该框架适用于任何静态、球对称、渐近平坦背景上的任意潮汐扰动，基于频率 $\omega$ 的幂次近区展开以及空间无穷远处的单值性。一个主递推公式确定了单值性生成元至 $\omega^2$ 的所有阶，其三个独立分量完全编码了 Love 数的跑动。这一结构解释了重整化群方程的二次性质，此处已对所有阶和任何类型的 Love 数进行了证明。我们讨论了对数系数的方案依赖性，单值性形式使其变得透明。特别地，这阐明了潮汐场的反常指数，即 Mano-Suzuki-Takasugi 形式中的“重整化角动量”，是方案不变的，并且可以在任何时空上直接计算，无需显式解。我们讨论了若干应用于黑洞的例子，包括推导 Reissner-Nordström 黑洞轴向 Love 数领先动力学跑动的闭式公式，特别证明了在极端极限下该跑动为零。对于超出 GR 的一般黑洞，我们证明了动力学跑动探测的是比静态更低多极子处的度规形变，并通过推导 Hayward 和 Bardeen 正则黑洞的一些精确结果来说明该方法的威力。
英文摘要
The static tidal Love numbers of black holes vanish in general relativity (GR), but are generically non-zero, and in fact 'run' logarithmically with scale, in more general theories or beyond the static limit. We expose a model-agnostic framework for the running of Love numbers at the dynamical level, valid for any tidal perturbation on any static, spherically symmetric, asymptotically flat background, based on the near-zone expansion in powers of the frequency $ω$ and on the monodromy at spatial infinity. A master recurrence formula determines the monodromy generator to all orders in $ω^2$, whose three independent entries fully encode the running of the Love numbers. This structure explains the quadratic nature of the renormalization group equation, here proved to all orders and for any type of Love number. We discuss the scheme dependence of the logarithmic coefficients, which is made transparent by the monodromy form. In particular, this clarifies that the anomalous exponents of the tidal field, the so-called 'renormalized angular momentum' of the Mano-Suzuki-Takasugi formalism, are scheme-invariant and directly computable on any spacetime, without need of explicit solutions. We discuss several applications to black holes, including the derivation of a closed-form formula for the leading dynamical running of axial Love numbers of Reissner-Nordström black holes, proving in particular that it vanishes in the extremal limit. For generic black holes beyond GR, we prove that dynamical running probes deformations of the metric at lower multipoles than the static one, and we illustrate the power of the method by deriving some exact results for the Hayward and Bardeen regular black holes.
Comments34 pages
