Possible resolution of a spacetime singularity with field transformations
Possible resolution of a spacetime singularity with field transformations
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通过场变换解决时空奇点的可能方法
DOI：
10.1093/ptep/ptaa028
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发表时间：
2020
影响因子：
3.5
通讯作者：
Misao Sasaki
中科院分区：
文献类型：
--
作者：
Atsushi Naruko;Chul-Moon Yoo;Misao Sasaki
人们普遍认为，经典引力是分解的，需要量子引力来处理奇点。我们证明了存在一类时空曲率奇点，它可以通过度规变换和物质场变换来解决。作为一个例子，我们考虑了一个具有标量场和规范场的各向异性幂定律膨胀模型，其中在时间开始时存在类空的曲率奇异性。首先，我们给出了度量到平坦几何的变换，即Minkowski度量。该变换消除了位于时间原点的曲率奇异性。与文献中以前的工作的一个本质区别是，时间的起源不是通过变换而被送到过去的无限，而是保持在过去的有限时间。这样，几何就可以超越奇点而变得可扩展。一般而言，物质场在经过这样的度规变换后仍保持其原始形式的奇异性。然而，我们明确地表明，在一种情况下，物质场的奇异行为可以通过物质场的重新定义来完全消除。因此，我们第一次解决了一类初始宇宙奇点，并成功地将时空扩展到经典引力框架下的奇点之外。
It is widely believed that classical gravity breaks down and quantum gravity is needed to deal with a singularity. We show that there is a class of spacetime curvature singularities which can be resolved with metric and matter field transformations. As an example, we consider an anisotropic power-law inflation model with scalar and gauge fields in which a space-like curvature singularity exists at the beginning of time. First, we provide a transformation of the metric to the flat geometry, i.e. the Minkowski metric. The transformation removes the curvature singularity located at the origin of time. An essential difference from previous work in the literature is that the origin of time is not sent to past infinity by the transformation but it remains at a finite time in the past. Thus the geometry becomes extensible beyond the singularity. In general, matter fields are still singular in their original form after such a metric transformation. However, we explicitly show that there is a case in which the singular behavior of the matter fields can be completely removed by a redefinition of matter fields. Thus, for the first time, we have resolved a class of initial cosmic singularities and successfully extended the spacetime beyond the singularity in the framework of classical gravity.