The process of the gravitational collapse might lead not only to a black hole but also to naked singularity formation. In this paper, we consider the generalized Vaidya spacetime with polytropic and generalized polytropic equations of state. We solve the Einstein and Einstein–Maxwell equations to obtain the explicit form of a mass function. We consider the limiting cases of solutions and find out, that generalized Vaidya spacetime might behave like Vaidya–de Sitter and Bonnor–Vaidya–de sitter solutions. Moreover, we explicitly show, that the part of solution, which depends on the polytropic index, is similar to cosmological fields surrounding both Vaidya and Bonnor–Vaidya black holes. The process of the gravitational collapse has been then considered. We have found out that the conditions of the naked singularity formation don’t depend on the polytropic index.

引力塌缩的过程不仅可能导致黑洞，还可能导致裸奇点的形成。在本文中，我们考虑具有多变性的广义 Vaidya 时空和广义多变状态方程。我们求解爱因斯坦和爱因斯坦-麦克斯韦方程以获得质量函数的显式形式。我们考虑解的极限情况，并发现广义 Vaidya 时空可能表现得像 Vaidya-de Sitter 和 Bonnor-Vaidya-de Sitter 解。此外，我们明确表明，取决于多方指数的解部分类似于 Vaidya 和 Bonnor-Vaidya 黑洞周围的宇宙场。然后考虑了引力塌缩的过程。我们发现裸奇点形成的条件并不依赖于多方指数。