守恒群几何中的暗物质-重子物质径向加速度关系
Dark Matter-Baryonic Matter Radial Acceleration Relationship in Conservation Group Geometry
摘要：
潘德雷斯发展了一种理论，通过一个具有扩大协方差群的正交四元组场来扩展真实四维时空的几何结构。这个新的群，称为守恒群，包含群的非同态作为一个适当的子群，我们假设它是量子几何的基础群。使用曲率向量$C_μ$，我们找到自由场拉格朗日密度$C^μC_μ\sqrt{-g}\,$。当有大质量物体存在时，源项被加到这个拉格朗日密度上。球对称解的自由场和场的源已被导出。场方程要求在没有源的区域存在非零应力-能量张量，因此可能以自然的方式引入暗物质和暗能量。给出了一个简单的星系模型，它满足我们的场方程。该模型包括平坦的旋转曲线。本文将我们的结果与最近报道的McGaugh，Lelli和Schombert的结果进行了比较，这些结果揭示了观测到的径向加速度与重子径向加速度之间的一个新的规律。我们发现了一个稍微不同的模型，它将这些加速度联系起来。结合我们的模型，McGaugh，Lelli和Schombert关系意味着一个新的临界重子加速。当应用于核球支配的星系时，这个临界重子加速度可以通过核球半径来预测径向速度曲线值。
英文摘要：
Pandres has developed a theory which extends the geometrical structure of a real four-dimensional space-time via a field of orthonormal tetrads with an enlarged covariance group. This new group, called the conservation group, contains the group of diffeomorphisms as a proper subgroup and we hypothesize that it is the foundational group for quantum geometry. Using the curvature vector, $C_μ$, we find a free-field Lagrangian density $C^μC_μ\sqrt{-g}\,$. When massive objects are present a source term is added to this Lagrangian density. Spherically symmetric solutions for both the free field and the field with sources have been derived. The field equations require nonzero stress-energy tensors in regions where no source is present and thus may bring in dark matter and dark energy in a natural way. A simple model for a galaxy is given which satisfies our field equations. This model includes flat rotation curves. In this paper we compare our results with recently reported results of McGaugh, Lelli and Schombert which exhibit a new law between the observed radial acceleration and the baryonic radial acceleration. We find a slightly different model which relates these accelerations. In conjunction with our model, the McGaugh, Lelli and Schombert relation imply a new critical baryonic acceleration. When applied to bulge-dominated galaxies, this critical baryonic acceleration may be used to predict the radial velocity curve value by using the radius of the bulge.
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