发表机构
Instituto de Astronomía, Universidad Nacional Autónoma de México; Centro de Astrofísica e Gravitação–CENTRA, Departamento de Física, Instituto Superior Técnico–IST, Universidade de Lisboa–UL（墨西哥国立自治大学天文研究所; 里斯本大学高等理工学院物理中心天体物理学与引力中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究在二次f(R)引力框架下，利用高斯-博内定理推导得出静态黑洞与同质量中子星的弱透镜特征存在本质差异，弱透镜可作为判别该引力理论的依据。
AI 中文摘要
二次f(R)引力包含一个有质量的标量自由度——标量子（scalaron），其有限范围λ会屏蔽它对致密天体外部几何的影响。我们证明，这种屏蔽将黑洞的外部区域与同质量中子星的外部区域分离开来。对史瓦西度规的修正为 Yukawa 衰减形式，随e^(-r/λ)下降，而非耦合的多项式形式，因此对该耦合的任何幂次展开都不可见；此外，该外部区域本质上是各向同性的，因此仅反转时间势（如单势解中那样）无法求解场方程。将高斯-博内定理应用于该几何，我们发现 leading 偏转角恰好是广义相对论的4GM/b，标量子贡献在使光弯曲的组合中完全抵消。首个修正项具有不寻常的特征λ^(-1/2)b^(-3/2)e^(-b/λ)，在标量子范围外被屏蔽，通过直接求积在b=4λ时验证精度约为20%，在b=12λ时提升至7%。剩余的不是程度差异而是种类差异。产生该差异的三个要素——耦合中的非解析性、本质上各向同性的规范以及压力加权标量电荷，首次在单一自洽推导中得到。静态黑洞无标量毛，其透镜行为完全符合广义相对论要求；中子星则获得由支撑其抵抗坍缩的压力加权的标量电荷，二者不同。因此，弱透镜成为该理论的判别依据，而视界（与物质表面相对）原则上仍是另一依据。观测优势不在于大b处的偏转角，而在于光子球的强场成像以及恒星内部，其中标量电荷由物态方程（EoS）确定。
英文摘要
Quadratic $f(R)$ gravity carries a massive scalar degree of freedom, the scalaron, whose finite range $λ$ screens its influence on the geometry outside a compact object. We show that this screening severs the exterior of a black hole from that of a neutron star of the same mass. The correction to the Schwarzschild metric is Yukawa-suppressed, falling as $e^{-r/λ}$ instead of polynomially in the coupling, and is thus invisible to any expansion in powers of that coupling; also, the exterior is intrinsically isotropic, so that inverting the temporal potential alone, as in single-potential solutions, fails to solve ]field equations. Applying the Gauss-Bonnet theorem to this geometry, we find the leading deflection angle to be exactly the general-relativistic $4GM/b$, the scalaron contributions cancelling identically in the combination that bends light. The first correction carries the unfamiliar signature $λ^{-1/2}b^{-3/2}e^{-b/λ}$, screened beyond the scalaron range and confirmed against direct quadrature to around 20% at $b=4λ$, improving to 7% at $b=12λ$. What survives is not a difference of degree but of kind. The three ingredients that deliver it, non-analyticity in the coupling, the intrinsically isotropic gauge and the pressure-weighted scalar charge, are here obtained within a single, self-consistent derivation for the first time. A static black hole carries no scalar hair, and lenses precisely as GR requires; a neutron star acquires a scalar charge weighted by the pressure supporting it against collapse, and does not. Weak lensing hence closes as a discriminant of the theory, whilst the horizon, as against a material surface, remains one in principle. The observational advantage lies not in bending angles at large $b$ but in the strong-field imaging of the photon sphere, and in the stellar interior, where the scalar charge is fixed by EoS.
Comments9 pages, 4 figures
