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.

中文翻译：

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通过场变换解决时空奇点

人们普遍认为经典引力会分解，需要量子引力来处理奇点。我们表明存在一类时空曲率奇点，可以用度量和物质场变换来解决。例如，我们考虑具有标量场和规范场的各向异性幂律膨胀模型，其中在开始时存在类似空间的曲率奇点。首先，我们将度量转换为平面几何，即Minkowski度量。该变换消除了位于时间起点的曲率奇点。与文献中先前工作的本质区别是，时间的起源不是通过变换传递到过去的无限，而是保留在过去的有限时间。因此，几何形状变得可扩展到超出奇点。通常，经过这样的度量转换后，物质场仍然以其原始形式是奇异的。但是，我们明确表明，在某些情况下，可以通过重新定义物质场来完全除去物质场的奇异行为。因此，我们首次解决了一类初始宇宙奇点，并成功地将时空扩展到了经典引力框架之外的奇点之外。