Pandres has shown that an enlargement of the covariance group to the group of conservative transformations leads to a richer geometry than that of general relativity. Using orthonormal tetrads as field variables, the fundamental geometric object is the curvature vector denoted by $$C_\mu $$ C μ . From an appropriate scalar Lagrangian field equations for both free-field and the field with sources have been developed. We first review models which use a free-field solution to model the Solar System and why these results are unacceptable. We also show that the standard Schwarzschild metric is also unacceptable in our theory. Finally we show that there are solutions which involve sources which agree with general relativity PPN parameters and thus approximate the Schwarzschild solution. The main difference is that the Einstein tensor is not identically zero but includes small values for the density, radial pressure and tangential pressure. Higher precision experiments should be able to determine the validity of these models. These results add further confirmation that the theory developed by Pandres is the fundamental theory of physics.

中文翻译：

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保守几何中的太阳系模型

Pandres 已经表明，将协方差群扩大到保守变换群会导致比广义相对论更丰富的几何。使用正交四分体作为场变量，基本几何对象是由 $$C_\mu $$C μ 表示的曲率向量。自由场和有源场的适当标量拉格朗日场方程已经被开发出来。我们首先回顾使用自由场解决方案来模拟太阳系的模型，以及为什么这些结果是不可接受的。我们还表明，标准 Schwarzschild 度量在我们的理论中也是不可接受的。最后，我们表明存在涉及与广义相对论 PPN 参数一致的源的解，因此近似于 Schwarzschild 解。主要区别在于爱因斯坦张量不是完全为零，而是包括密度、径向压力和切向压力的小值。更高精度的实验应该能够确定这些模型的有效性。这些结果进一步证实了潘德雷斯发展的理论是物理学的基础理论。