GENERAL RELATIVITY AND WEYL FRAMES
GENERAL RELATIVITY AND WEYL FRAMES
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DOI：
10.1142/s2010194511001115
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发表时间：
2011-06
期刊：
影响因子：
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通讯作者：
C. Romero;J. B. Fonseca-Neto;M. L. Pucheu
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作者：
C. Romero;J. B. Fonseca-Neto;M. L. Pucheu
我们用一种非黎曼几何，即魏尔几何的语言来介绍广义相对论。我们通过使用Weyl框架的概念表明，新的数学形式可以导致相同引力现象的不同图像。我们证明，在这种形式中，有可能构造一个标量张量引力理论，它对所谓的Weyl变换是不变的，并在一个特定的坐标系中简化为广义相对论，黎曼坐标系。在这种方法中，Weyl几何起着基本的作用，因为当在任意框架中观察时，它似乎是理论的自然几何设置。我们的出发点是构建一个对于Weyl转换明显不变的操作。当这个作用用更熟悉的黎曼几何术语来表示时，我们发现这个理论与布兰斯-迪克引力理论有一些相似之处。我们用一个例子来说明这一点，在这个例子中，当在特定的Weyl框架中重新解释时，可能会出现已知的Brans-Dicke真空溶液。
We present the general theory of relativity in the language of a non-Riemannian geometry, namely, Weyl geometry. We show that the new mathematical formalism may lead to different pictures of the same gravitational phenomena, by making use of the concept of Weyl frames. We show that, in this formalism, it is possible to construct a scalar-tensor gravitational theory that is invariant with respect to the so-called Weyl tranformations and reduces to general relativity in a particular frame, the Riemann frame. In this approach the Weyl geometry plays a fundamental role since it appears as the natural geometrical setting of the theory when viewed in an arbitrary frame. Our starting point is to build an action that is manifestly invariant with respect to Weyl transformations. When this action is expressed in more familiar terms of Riemannian geometry we find that the theory has some similarities with Brans-Dicke theory of gravity. We illustrate this point with an example in which a known Brans-Dicke vacuum solution may appear when reinterpreted in a particular Weyl frame.