黑洞模的绝热变形：II. 磁性GHS族
Adiabatic Deformations of Black Hole Moduli: II. The Magnetic GHS Family
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中文总结 AI 辅助
本文研究无质量爱因斯坦-麦克斯韦-伸缩子理论中磁性GHS黑洞的主导绝热响应，实现了正则切片与Fredholm框架，证明了相关泛函正定性，求解了受迫径向方程，给出了完整主导阶准静态近区响应。
中文摘要 AI 辅助
我们研究无质量爱因斯坦-麦克斯韦-伸缩子理论中，磁性GHS黑洞对在超前时间缓慢变化的指定外部模的主导绝热响应。采用带有精确面积半径的超前Eddington-Finkelstein坐标，我们推导了含时球对称方程，并对缓慢演化的瞬时静态GHS代表进行展开，使其视界与精确动力学边际视界区分开。磁性GHS族实现了姊妹论文中发展的正则切片与Fredholm框架，其可积性以闭式形式给出正则切向量、有限秩源分布、辅助非齐次方程的视界正则解，以及切片算子核的全局正则生成元。对于无质量大半径重叠中出现的主导Robin泛函，我们解析计算了Fredholm分母，并证明其在带电非极端支上严格为正；在核生成元的常规归一化退化处该性质仍成立，表明这些位点是归一化奇点而非核模的简并。在受控大半径重叠区域内，此正定性证明了完整主导阶准静态近区问题的存在性与唯一性，随后我们显式求解了受迫径向方程。标量滞后量是通用受迫分布与切片齐次模的和，其振幅由外部匹配数据确定；质量滞后量由径向约束代数推导，时滞由单次初等积分得到，经滞后修正的解可恢复精确边际视界。该结果为指定无质量重叠模型内所有容许的外部数据，提供了径向依赖精确的完整主导阶准静态近区响应。
英文摘要
We study the leading adiabatic response of magnetic GHS black holes in massless Einstein-Maxwell-dilaton theory to a prescribed exterior modulus varying slowly in advanced time. In ingoing Eddington-Finkelstein coordinates with the exact areal radius, we derive the time-dependent spherical equations and expand about a slowly evolving instantaneous static GHS representative, keeping its horizon distinct from the exact dynamical marginal horizon. The magnetic GHS family realizes the canonical-slice and Fredholm framework developed in the companion paper. Its integrability yields in closed form the canonical tangent, the finite-rank source profile, a horizon-regular solution of the auxiliary inhomogeneous equation, and a globally regular generator of the sliced-operator kernel. For the leading Robin functional arising in the massless large-radius overlap, we evaluate the Fredholm denominator analytically and prove that it is strictly positive on the charged non-extremal branch. This remains true where the conventional normalization of the kernel generator degenerates, showing that these loci are normalization singularities rather than degeneracies of the kernel mode. Within the controlled large-radius overlap regime, this positivity proves existence and uniqueness of the completed leading-order quasi-static near-zone problem. We then solve the forced radial equation explicitly. The scalar lag is the sum of a universal forced profile and a sliced homogeneous mode whose amplitude is fixed by the exterior matching datum. The mass lag follows algebraically from the radial constraint, and the lapse lag from a single elementary quadrature. The exact marginal horizon is recovered from the lag-corrected solution. The result gives the complete leading quasi-static near-zone response, exact in its radial dependence, for every admissible exterior datum within the specified massless overlap model.
