在银河系中心黑洞附近解除 f(R) 引力：通过近日点移位在 S0-2 轨道以下进行可检验性测试
Unscreening of f(R) gravity near the galactic center black hole: Testability through pericenter shift below S0-2's orbit
AI总结：
研究在银河系中心黑洞附近通过近日点移位测试 f(R) 引力，发现轻质和中间质量标量场在 S0-2 轨道附近未被屏蔽，可能通过 ELTs 检测其效应。
摘要：
广义相对论（GR）在太阳系中已被广泛测试，并正在银河系中心（GC）黑洞的新环境中进行测试，其中无量纲引力势（GM/c²r）是太阳系中遇到的100倍。因此，GC黑洞的邻近区域是一个测试修改引力理论的自然机会。在本工作中，研究了接近黑洞的 f(R) 引力效应。对于具有半长轴等于或低于 a=1000 au（S0-2 类轨道）的紧凑轨道，研究了 GR 与 f(R) 引力之间的近日点移位差异。在模型依赖的方法中，我们选择 f(R) ∝ R²（幂律引力）模型，该模型具有宇宙学动机，并研究了黑洞零自转和非零自转情况下的轨道近日点移位偏差。发现 f(R) 引力效应在紧凑轨道中尤为显著。在 f(R) 引力的模型无关方法中，通过通用标量场（ψ=f'(R)）提取 f(R) 引力的参数，从当前的参数后牛顿（PPN）参数（γ, β）的界限中进行研究。还研究了这些 PPN 参数的界限下的 f(R) 引力屏蔽情况。发现足够质量的标量场（10^-16 eV）完全被屏蔽，但轻质和中间质量的标量场（10^-22 eV 和 10^-19 eV）在 S0-2 类轨道以及新发现的短周期星 S4716（a=407 au）的轨道中未被屏蔽。通过现有和即将来临的极大望远镜（ELTs）的测星能力，预测了这些未屏蔽标量场导致的 f(R) 引力效应的检测可能性。
英文摘要：
General Relativity (GR) has been tested extensively in the solar system and is being tested in the new environment of the Galactic Centre (GC) black hole where the dimensionless gravitational potential ($GM/c^2r$) is 100 times stronger than the one encountered in solar system. Therefore, the neighbourhood of the GC black hole is a naive opportunity to test modified theories of gravity. In this work, effect of $f(R)$ gravity near the black hole is studied. The difference of pericentre shift between GR and $f(R)$ gravity is studied for compact orbits having semi-major axis equal to and below $a=1000$ au (S0-2 like orbits). In a model dependent approach, we choose $f(R) \propto R^2$ (power law gravity) model which is cosmologically motivated and study the deviation in orbital pericentre shift for both zero spin and non-zero spin of the black hole. It is found that effect of $f(R)$ gravity becomes prominent for compact orbits. In model independent approach to $f(R)$ gravity with the generic scalaron fields ($ψ=f'(R)$), we extract the parameters of $f(R)$ gravity from the current bounds on Parametrised Post Newtonian (PPN) parameters ($γ, β$) near the GC black hole. The screening of $f(R)$ gravity is also investigated for these bounds on PPN parameters. It has been found that sufficiently massive scalarons ($10^{-16}$ eV) are completely screened but light and intermediate mass scalarons ($10^{-22}$ eV and $10^{-19}$ eV) are unscreened towards S0-2 like orbits as well as in the orbit of the newly discovered short period star S4716 ($a=407$ au). The possibility of detection of the $f(R)$ gravity effects due to these unscreened scalarons is forecasted with existing and upcoming astrometric capabilities of Extremely Large Telescopes (ELTs).
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