发表机构
De La Salle University（德拉萨大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明约化MOG黑洞理论中线性标量扰动可退耦，且标量激发不改变临界曲线，而矢量扰动产生低频度规响应，区别于旋转效应。
AI 中文摘要
在约化强场理论中，当$\u03bc\bar G M\ll1$时，Schwarzschild-MOG黑洞的线性扰动在领头阶可分离为标量扇区和引力-矢量扇区。场重定义$\widehat h_{\u03bc\u03bd}=h_{\u03bc\u03bd}-\u03c8\bar g_{\u03bc\u03bd}$给出了标量的解耦Klein-Gordon方程以及引力-矢量扇区的Reissner-Nordström方程。在给定的谱边界条件下，对于$m_G^2\ge0$，标量是稳定的。纯标量激发产生共形度规扰动，其零哈密顿贡献为$H_1^{(s)}=-\u03c8 H_0$。对于固定的观测者世界线和共形对应的正交标架，只要共形因子光滑、为正且保持俘获边界，每个线性标量到临界曲线的转移系数都为零，包括单极呼吸模式。特殊的带电轴向偶极子则诱导受约束的度规扰动。一阶径向积分可在未来视界和球面上规范正则的规范中重构该扰动，将辐射振幅与平稳角动量分离，无需除以频率。对于具有零角动量的单位入射正则矢量振幅，匹配渐近解给出了显式的电荷依赖的局部度规响应，在固定半径和固定次极端背景下该响应随$\u03c9^2$趋于零。一个独立的无穷小Kerr-Newman基准给出了平稳碰撞参数中点位移，并在中性极限下恢复$\u03b4C_b=-2a_{\rm rot}$。这些结果排除了指定角临界曲线的线性标量呼吸，并将低频矢量诱导的度规响应与平稳旋转效应区分开来。
英文摘要
Linear perturbations of a Schwarzschild-MOG black hole separate into scalar and gravito-vector sectors in the reduced strong-field theory at leading order in $μ\bar G M\ll1$. The field redefinition $\widehat h_{μν}=h_{μν}-ψ\bar g_{μν}$ gives a decoupled Klein--Gordon equation for the scalar and the Reissner--Nordström equations for the gravito-vector sector. The scalar is stable under the stated spectral boundary conditions for $m_G^2\ge0$. A scalar-only excitation produces a conformal metric perturbation with null Hamiltonian contribution $H_1^{(s)}=-ψH_0$. For fixed observer worldlines and conformally corresponding orthonormal frames, every linear scalar-to-critical-curve transfer coefficient vanishes, including monopole breathing, provided the conformal factor is smooth, positive, and preserves the capture boundary. The exceptional charged axial dipole instead induces a constrained metric perturbation. A first-order radial integral reconstructs this perturbation in a gauge regular at the future horizon and on the sphere, separating the radiative amplitude from stationary angular momentum without division by frequency. For a unit-incident canonical vector amplitude with zero angular momentum, matched asymptotic solutions give an explicit charge-dependent local metric response that vanishes as $ω^2$ at fixed radius and fixed subextremal background. A separate infinitesimal Kerr--Newman benchmark yields the stationary impact-parameter midpoint shift and recovers $δC_b=-2a_{\rm rot}$ in the neutral limit. These results exclude linear scalar breathing of the specified angular critical curve and distinguish the low-frequency vector-induced metric response from a stationary rotation effect.
