LyST：Lyra流形上的引力标量张量理论
LyST: a Scalar-Tensor Theory of Gravity on Lyra Manifold
摘要：
本文在无挠度规相容的Lyra流形上给出了引力的标量张量理论。这是通过考虑定义在流形上的尺度函数来推广物理参考系的概念而获得的。一个特定的框架的选择诱导一个本地基地，自然非完整的，其结构常数引起额外的条款的连接系数的表达和协变导数的表达。在天琴座流形中，涉及坐标和尺度的参考系之间的变换改变了张量场的变换规律，与黎曼流形相比。从爱因斯坦-希尔伯特最小作用量与物质项耦合的直接推广，可以建立一个天琴座不变作用量，这产生了相关的天琴座标量-张量引力理论（LyST），以及$g_{μν}$和$ϕ$的场方程。这些方程有一个很好的牛顿极限，由此可以看出度规和标度在描述引力相互作用中都起作用。我们提出了LyST重力场方程的球对称解。它依赖于两个参数$m$和$r_{L}$，并详细研究了它们的物理意义.我们突出LyST球对称线元的性质，并将其与Schwarzchild解进行比较。
英文摘要：
We present a scalar-tensor theory of gravity on a torsion-free and metric compatible Lyra manifold. This is obtained by generalizing the concept of physical reference frame by considering a scale function defined over the manifold. The choice of a specific frame induces a local base, naturally non-holonomic, whose structure constants give rise to extra terms in the expression of the connection coefficients and in the expression for the covariant derivative. In the Lyra manifold, transformations between reference frames involving both coordinates and scale change the transformation law of tensor fields, when compared to those of the Riemann manifold. From a direct generalization of the Einstein-Hilbert minimal action coupled with a matter term, it was possible to build a Lyra invariant action, which gives rise to the associated Lyra Scalar-Tensor theory of gravity (LyST), with field equations for $g_{μν}$ and $ϕ$. These equations have a well-defined Newtonian limit, from which it can be seen that both metric and scale play a role in the description gravitational interaction. We present a spherically symmetric solution for the LyST gravity field equations. It dependent on two parameters $m$ and $r_{L}$, whose physical meaning is carefully investigated. We highlight the properties of LyST spherically symmetric line element and compare it to Schwarzchild solution.
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