论文标题
连接的非现象是如何自然出现的。
How the non-metricity of the connection arises naturally in the classical theory of gravity
论文作者
论文摘要
时空的几何形状由两个 - {\ em a Independent -dipption -几何结构：对称连接$γ$和公制张量$ g $描述。 Palatini变分原理暗示了$γ$（即$ \ nabla g = 0 $）的度量条件，但仅当物质字段属于特殊类别时。如果有通用物质领域，帕拉蒂尼（Palatini）表示$γ$的非金属性。传统上，我们在这种情况下使用（第二阶）希尔伯特原理，而不是（一阶）palatini原则，假设标准条件{\ em a a a priori}。不幸的是，爱因斯坦方程的产生右侧与物质能量量张量不一致。我们建议认真对待palatini impl的非金属连接。传统的爱因斯坦理论是根据该对象重写的，它获得了更简单和普遍的结构。这种方法为描述大规模效应（深色物质？，暗能量？）打开了一个空间，而无需在引力领域的拉格朗日中纯粹遵守现象学术语。本文中讨论的所有理论都属于标准的一般相对论理论，唯一的非标准要素是它们（更简单）的数学表述。作为数学奖励，我们在变化的计算中提出了一种新的形式主义，因为在双曲线野外理论的情况下，标准方法导致了无意义的结论。
Spacetime geometry is described by two -- {\em a priori} independent -- geometric structures: the symmetric connection $Γ$ and the metric tensor $g$. Metricity condition of $Γ$ (i.e. $\nabla g = 0$) is implied by the Palatini variational principle, but only when the matter fields belong to an exceptional class. In case of a generic matter field, Palatini implies non-metricity of $Γ$. Traditionally, instead of the (1st order) Palatini principle, we use in this case the (2nd order) Hilbert principle, assuming metricity condition {\em a priori}. Unfortunately, the resulting right-hand side of the Einstein equations does not coincide with the matter energy-momentum tensor. We propose to treat seriously the Palatini-implied non-metric connection. The conventional Einstein's theory, rewritten in terms of this object, acquires a much simpler and universal structure. This approach opens a room for the description of the large scale effects in General Relativity (dark matter?, dark energy?), without resorting to purely phenomenological terms in the Lagrangian of gravitational field. All theories discussed in this paper belong to the standard General Relativity Theory, the only non-standard element being their (much simpler) mathematical formulation. As a mathematical bonus, we propose a new formalism in the calculus of variations, because in case of hyperbolic field theories the standard approach leads to nonsense conclusions.
