It is well known that static wormhole configurations in general relativity (GR) are possible only if matter threading the wormhole throat is “exotic”—i.e., violates a number of energy conditions. For this reason, it is impossible to construct static wormholes supported only by dust-like matter which satisfies all usual energy conditions. However, this is not the case for non-static configurations. In 1934, Tolman found a general solution describing the evolution of a spherical dust shell in GR. In this particular case, Tolman’s solution describes the collapsing dust ball; the inner space-time structure of the ball corresponds to the Friedmann universe filled by a dust. In the present work we use the general Tolman’s solution in order to construct a dynamic spherically symmetric wormhole solution in GR with dust-like matter. The solution constructed represents the collapsing dust ball with the inner wormhole space-time structure. It is worth noting that, with the dust-like matter, the ball is made of satisfies the usual energy conditions and cannot prevent the collapse. We discuss in detail the properties of the collapsing dust wormhole.

中文翻译：

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尘埃状物质造成的坍塌虫洞

众所周知，只有将虫孔喉部穿线的物质“外来”（即违反了许多能量条件）时，广义相对论（GR）中的静态虫孔配置才有可能。因此，不可能构造仅由满足所有常规能量条件的粉尘状物质支撑的静态虫洞。但是，对于非静态配置则不是这种情况。1934年，托尔曼（Tolman）找到了描述球形尘壳在GR中演变的一般解决方案。在这种特殊情况下，托尔曼的解决方案描述了坍塌的尘球。球的内部时空结构与充满灰尘的弗里德曼宇宙相对应。在当前工作中，我们使用通用的Tolman解来构造具有粉尘状物质的GR中的动态球对称虫孔解决方案。构造的解表示具有内部虫洞时空结构的坍塌尘埃球。值得注意的是，对于球状粉尘来说，球是由通常的能量条件制成的，无法防止球体塌陷。我们将详细讨论坍塌的粉尘虫洞的特性。