论文标题
非欧几里得牛顿宇宙学
Non-Euclidean Newtonian Cosmology
论文作者
论文摘要
在假设牛顿的绝对空间是非欧几里得的假设下，我们提出并解决了牛顿宇宙学的问题。特别是，我们专注于负弯曲的双曲线空间H3。我们指出，欧几里得空间中牛顿宇宙学的弗里德曼方程中产生的曲率项与曲率在H3空间中的作用之间的不等性。我们发现反方法律的概括以及随之而来的牛顿宇宙学的解决方案。我们发现H3中欧几里得米歇尔“黑洞”的概括，并表明它导致了与我们在一般相对论中发现的最大力和面积不同的结果。我们展示了如何将宇宙常数的对应物添加到H3中的重力潜力，并探索导致宇宙学模型的解决方案和渐近线。我们还讨论了具有非负空间曲率的牛顿宇宙学引入紧凑拓扑的问题。
We formulate and solve the problem of Newtonian cosmology under the assumption that the absolute space of Newton is non-Euclidean. In particular, we focus on the negatively-curved hyperbolic space, H3. We point out the inequivalence between the curvature term that arises in the Friedmann equation in Newtonian cosmology in Euclidean space and the role of curvature in the H3 space. We find the generalisation of the inverse-square law and the solutions of the Newtonian cosmology that follow from it. We find the generalisations of the Euclidean Michell 'black hole' in H3 and show that it leads to different maximum force and area results to those we have found in general relativity. We show how to add the counterpart of the cosmological constant to the gravitational potential in H3 and explore the solutions and asymptotes of the cosmological models that result. We also discuss the problems of introducing compact topologies in Newtonian cosmologies with non-negative spatial curvature.
