太阳系与银心处的非最小耦合Weyl联络引力
Non-minimally coupled Weyl connection gravity in the Solar System and at the Galactic Center
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中文总结 AI 辅助
该研究探讨非最小耦合Weyl联络引力的可行性，推导两类Schwarzschild类真空解的参数约束，从太阳系测试和银心S2星观测得到ω的严格下界，为该引力理论提供观测限制。
中文摘要 AI 辅助
我们通过将非最小耦合Weyl联络引力的静态球对称黑洞解与经典弱场太阳系测试及Sgr A*附近的恒星轨道观测相对比，探究该理论的现象学可行性。在这一几何框架中，非度量性通过Weyl矢量场编码，产生两类不同的Schwarzschild类真空解，其特征为具有长度量纲的自由参数ω。我们计算了四个经典观测量——引力红移、水星近日点进动、光线偏折及雷达回波延迟的修正项，并利用当前观测数据推导了ω的严格下界。对于第一类解（纯径向Weyl矢量），主导度规修正项按1/ω缩放，从近日点进动可得到ω≳10³⁰ m的强约束；对于第二类解（时-径向Weyl矢量），修正项按1/ω²缩放，约束更弱，从同一测试得到ω≳10²⁰ m的结果。这一显著差异源于两类解中线性项的不同行为：第一类解存在不受抑制的线性项2r/ω，在太阳系区域占主导；第二类解的线性项额外受M/ω因子抑制，使得二次项-r²/(4ω²)在整个区域占主导。随后我们分析了银心附近的恒星轨道，发现当前S2星的观测对两类解提供了互补约束。
英文摘要
We explore the phenomenological viability of non-minimally coupled Weyl connection gravity by confronting its static, spherically symmetric black hole solutions with classical weak-field Solar System tests and stellar-orbit observations near Sgr A*. In this geometric framework, non-metricity is encoded via a Weyl vector field, giving rise to two distinct families of Schwarzschild-like vacuum solutions characterized by a free parameter \(ω\) with dimensions of length. We compute the corrections to four classical observables---gravitational redshift, Mercury's perihelion advance, light deflection, and radar echo delay---and derive stringent lower bounds on \(ω\) using current observational data. For Solution I (purely radial Weyl vector), the leading metric corrections scale as \(1/ω\), yielding bounds as strong as \(ω\gtrsim 10^{30}\) m from perihelion precession. For Solution II (time-radial Weyl vector), the corrections scale as \(1/ω^2\), resulting in weaker constraints, with \(ω\gtrsim 10^{20}\) m from the same test. This marked difference arises from the distinct behavior of the linear corrections in each solution: while Solution I exhibits an unsuppressed linear term \(2r/ω\) that dominates in the Solar System regime, Solution II features a linear term suppressed by an additional factor of \(M/ω\), making the quadratic term \(-r^2/4ω^2\) dominant throughout. We then analyze stellar orbits near the Galactic Center, finding that current observations of the S2 star provide complementary constraints on both solutions. (...)
