论文标题
1+3-Newton-Cartan系统和Newton-Cartan宇宙学
The 1+3-Newton-Cartan system and Newton-Cartan cosmology
论文作者
论文摘要
我们执行牛顿 - 卡丹方程的协变量1+3分。所得的3维方程系统，称为\ textit {1+3-Newton-cartan方程}，在结构上等同于1+3-Einstein方程。特别是它具有动量约束，并且适应坐标的选择对应于移动向量的选择。我们表明，这些方程将减少到经典的牛顿方程，而无需特殊的伽利略坐标。如果假定空间是紧凑的，则1+3-Newton-Cartan方程的解相当于经典牛顿方程的解决方案。然后，我们表明，空间扩展是牛顿 - 卡丹理论中的一个基本领域，而不是像牛顿宇宙学的经典表述那样建立。我们恢复了牛顿宇宙学一般扩张法的Buchert-ehlers定理。
We perform a covariant 1+3 split of the Newton-Cartan equations. The resulting 3-dimensional system of equations, called \textit{the 1+3-Newton-Cartan equations}, is structurally equivalent to the 1+3-Einstein equations. In particular it features the momentum constraint, and a choice of adapted coordinates corresponds to a choice of shift vector. We show that these equations reduce to the classical Newton equations without the need for special Galilean coordinates. The solutions to the 1+3-Newton-Cartan equations are equivalent to the solutions of the classical Newton equations if space is assumed to be compact or if fall-off conditions at infinity are assumed. We then show that space expansion arises as a fundamental field in Newton-Cartan theory, and not by construction as in the classical formulation of Newtonian cosmology. We recover the Buchert-Ehlers theorem for the general expansion law in Newtonian cosmology.
