在内部 STEGR 形式中重新审视重合广义相对论
Revisiting Coincident GR in Internal STEGR Formulation
AI总结：
基于内部空间形式的 STEGR 规范引力方法重新审视 CGR，回顾其标准形式，推导规范方法中的场方程并讨论相关问题，在重合规范下从多方面推导 CGR 并给出测试标量粒子运动。
摘要：
我们基于对称平移等效于广义相对论（STEGR）的规范引力方法，在内部空间形式中重新审视重合广义相对论（CGR），这是作者之一最近在文献[J. Math. Phys. 66 (2025) 5, 052505]中提出的。首先回顾了帕拉蒂尼引力方法中 STEGR 理论的标准形式，通过拉格朗日乘子施加平移和无挠条件。接着引入规范引力方法中的 STEGR 理论并推导其场方程，讨论了奥斯特罗格拉德斯基鬼不稳定性，发现该理论可能需要施加退化条件。最后在重合规范下，从作用积分和场方程两方面推导 CGR，并讨论了 STEGR 理论可能的运动学，给出了测试标量粒子在非度规时空中的运动。
英文摘要：
We revisit Coincident General Relativity (CGR) in the gauge approach to gravity based on Symmetric Teleparallel Equivalent to General Relativity (STEGR) in the \textit{internal-space formulation}, which one of the authors recently proposed in Ref.~[J. Math. Phys. 66 (2025) 5, 052505]. First, we review the standard formulation of STEGR theories in the Palatini approach to gravity, in which formulation we impose the teleparallel and torsion-free conditions by using Lagrange multipliers. Second, we introduce the STEGR theories in the gauge approach to gravity, which is formulated in the internal space, and derive its field equations. We briefly discuss whether the Ostrogradski ghost instability exists and find that the theory may require a degenerate condition to be imposed. Finally, assuming the coincident gauge, we derive CGR in both terms of the action integral and the field equation. Discussing the possible kinematics of the STEGR theory, we formulate a motion of a test scalar particle in the spacetime with non-metricity.
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