A novel class of vacuum metrics expressible in analytical form was recently found for pure ℛ² gravity, based on a groundwork put forth by Buchdahl in 1962. These Buchdahl-inspired solutions offer a practical framework for testing ℛ² gravity through empirical observations. Within a subclass of asymptotically flat Buchdahl-inspired vacuum spacetimes, we identified a parameter ϵ measuring the deviation from the classic Schwarzschild metric, which corresponds to ϵ=0. In this paper, we employ observational data from the S2 star's orbit around Sgr A* in the Milky Way galactic center and perform Monte Carlo Markov Chain simulations to probe the effects of the new metrics on the orbit of the S2 star. Our analysis presented herein reports a range at 95% confidence level on the deviation parameter as ϵ ∈ (-0.6690, 0.4452). While no decisive evidence either in favor or in disfavor of the asymptotically flat Buchdahl-inspired spacetimes has been achieved, the obtained bound is compatible with the tighter results using other data of different nature as recently reported in Eur. Phys. J. C 84 (2024) 330. As a meaningful test probing into a strong-field regime, our present study calls for further observations with prolonged period and improved accuracy in order to tighten the bound for ϵ using the S2 star orbit.

中文翻译：

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银河系中心S2星ℛ2时空观测测试


最近，基于 Buchdahl 于 1962 年提出的基础工作，发现了一类可以以分析形式表达的新型真空度量，用于纯 ℛ ²引力。这些受 Buchdahl 启发的解决方案为通过经验观察测试 ℛ ²引力提供了实用的框架。在受布赫达尔启发的渐近平坦真空时空的一个子类中，我们确定了一个参数 ϵ，用于测量与经典史瓦西度量的偏差，对应于 ϵ=0。在本文中，我们利用银河系中心 Sgr A* 周围 S2 恒星轨道的观测数据，并进行蒙特卡洛马尔可夫链模拟，以探讨新指标对 S2 恒星轨道的影响。我们在此提出的分析将偏差参数 ε ε (-0.6690, 0.4452) 报告为 95% 置信水平的范围。虽然没有获得支持或反对布赫达尔启发的渐近平坦时空的决定性证据，但所获得的界限与使用不同性质的其他数据得出的更严格的结果相一致，如最近报道的欧元。物理。 J·C 84 (2024) 330. 作为对强场状态的一项有意义的测试探测，我们目前的研究要求进一步延长观测时间并提高精度，以便使用 S2 星轨道收紧 ϵ 的界限。