关于牛顿定律的拓扑修正
On Topological Modifications of Newton's Law
摘要：
最近的宇宙学数据非常大的距离挑战标准宇宙学模型的有效性。受观测到的空间平坦性、加速膨胀和宇宙中具有优先轴的各种各向异性的启发，我们研究了三维空间具有全局R^2 X S^1拓扑结构这一简单假设的结果。我们把紧化的半径作为观测到的宇宙尺度，超过这个尺度，加速膨胀就开始了。我们导出了对牛顿引力势的诱导修正，发现对于小于S^1-半径的距离，1/r-项可以用多极形式的收敛幂级数在极角上进行修正，从而使诱导各向异性在紧化的第三维中得到明确的表达。另一方面，对于比紧化尺度更大的距离，势的渐近行为表现出对数依赖性，具有指数小的修正。牛顿力从1/r^2到1/r的变化意味着宇宙膨胀的减速减弱。这样的拓扑结构也可以通过沿着对称轴具有周期性的标准牛顿轴对称质量分布局部地创建。在这种情况下，我们可以使用我们的结果来获得可测量的修改牛顿轨道的小距离和平坦的旋转光谱，在银河系的大距离。
英文摘要：
Recent cosmological data for very large distances challenge the validity of the standard cosmological model. Motivated by the observed spatial flatness the accelerating expansion and the various anisotropies with preferred axes in the universe we examine the consequences of the simple hypothesis that the three-dimensional space has a global R^2 X S^1 topology. We take the radius of the compactification to be the observed cosmological scale beyond which the accelerated expansion starts. We derive the induced corrections to the Newton's gravitational potential and we find that for distances smaller than the S^1-radius the leading 1/r-term is corrected by convergent power series of multipole form in the polar angle making explicit the induced anisotropy by the compactified third dimension. On the other hand, for distances larger than the compactification scale the asymptotic behavior of the potential exhibits a logarithmic dependence with exponentially small corrections. The change of Newton's force from 1/r^2 to 1/r behavior implies a weakening of the deceleration for the expanding universe. Such topologies can also be created locally by standard Newtonian axially symmetric mass distributions with periodicity along the symmetry axis. In such cases we can use our results to obtain measurable modifications of Newtonian orbits for small distances and flat rotation spectra, for large distances at the galactic level.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
