论文标题
牛顿分数量度重力和蒙德
Newtonian Fractional-Dimension Gravity and MOND
论文作者
论文摘要
本文基于分数维空间理论及其在牛顿重力的应用，引入了重力的替代模型。特别是，高斯的重力法和其他基本古典法律已扩展到$ d $维度的度量空间，其中$ d $可以是非整体维度。 我们展示了这种牛顿分数维度重力（NFDG）与修改后的牛顿动力学（MOND）之间的可能联系，这是一个领先的替代重力模型，它说明了观察到的星系和其他天体物理结构的特性，而无需暗物质假设。 mond加速度常数$ a_ {0} \ simeq 1.2 \ times 10^{-10} \ mbox {m} \ thinspace \ mbox \ mbox {s}^{-2} $可以与自然尺度长度$ l_ {0} $在nfdg中，即gm/l_ {0}^{2} $，用于质量$ m $的天体物理结构，并且深色制度存在于空间区域中，其中尺寸降低至$ d \ $ d \ 2 $。 对于几个基本的球形对称结构，我们比较了MOND的结果，例如经验径向加速关系（RAR），圆形速度图和观察到的径向加速度的对数图$ g_ {obs} $vs。baryonicradial radial加速度$ g_ $ g_ {bar} $ a {bar} $，with nfdg rescess。我们表明，我们的模型能够使用可变的局部尺寸$ d \ left（w \ right）$重现这些结果，其中$ w = r/l_ {0} $是无尺寸的径向坐标。目前，我们无法从第一原理中明确得出此维度函数$ d \ left（w \ right）$，但是在每种情况下，从一般RAR中可以通过经验获得它。 该受试者的其他工作，包括轴对称结构的研究，详细的银河旋转曲线拟合以及可能的相对论扩展，以建立NFDG作为可行的重力替代模型。
This paper introduces a possible alternative model of gravity based on the theory of fractional-dimension spaces and its applications to Newtonian gravity. In particular, Gauss's law for gravity as well as other fundamental classical laws are extended to a $D$-dimensional metric space, where $D$ can be a non-integer dimension. We show a possible connection between this Newtonian Fractional-Dimension Gravity (NFDG) and Modified Newtonian Dynamics (MOND), a leading alternative gravity model which accounts for the observed properties of galaxies and other astrophysical structures without requiring the dark matter hypothesis. The MOND acceleration constant $a_{0} \simeq 1.2 \times 10^{ -10}\mbox{m}\thinspace \mbox{s}^{ -2}$ can be related to a natural scale length $l_{0}$ in NFDG, i.e., $a_{0} \approx GM/l_{0}^{2}$, for astrophysical structures of mass $M$, and the deep-MOND regime is present in regions of space where the dimension is reduced to $D \approx 2$. For several fundamental spherically-symmetric structures, we compare MOND results, such as the empirical Radial Acceleration Relation (RAR), circular speed plots, and logarithmic plots of the observed radial acceleration $g_{obs}$ vs. the baryonic radial acceleration $g_{bar}$, with NFDG results. We show that our model is capable of reproducing these results using a variable local dimension $D\left (w\right )$, where $w =r/l_{0}$ is a dimensionless radial coordinate. At the moment, we are unable to derive explicitly this dimension function $D\left (w\right )$ from first principles, but it can be obtained empirically in each case from the general RAR. Additional work on the subject, including studies of axially-symmetric structures, detailed galactic rotation curves fitting, and a possible relativistic extension, will be needed to establish NFDG as a viable alternative model of gravity.
