As realistic objects in the Universe, the black holes are surrounded by complex environment. By taking the effect of thermal environment into account, we investigate the evaporation process and the time evolutions (page curves) of the entanglement entropies of Hawking radiation of various types of black holes. It is found that the black holes with the thermal environments evaporate slower than those without the environments due to the environmental contribution of the energy flux in addition to Hawking radiation. For Schwarzschild black hole and Reissner-Nordstrm black hole in flat spaces, when the initial temperature of the black hole is higher than the environment temperature, the black holes evaporate completely and the Hawking radiation is eventually purified. For Schwarzschild-AdS black hole, it will evaporate completely and the Hawking radiation is purified when the environment temperature is lower than the critical temperature. Otherwise, it will reach an equilibrium state with the environment and the radiation is maximally entangled with the black hole. Our results indicate that the final state of the black hole is determined by the environmental temperature and the temporal evolution and the speed of the information purification process characterized by the page curve of the Hawking radiation is also influenced by the thermal environment significantly.

黑洞作为宇宙中的现实物体，被复杂的环境所包围。通过考虑热环境的影响，我们研究了各种类型黑洞的霍金辐射纠缠熵的蒸发过程和时间演化（页面曲线）。研究发现，由于能量通量和霍金辐射的环境贡献，有热环境的黑洞比没有热环境的黑洞蒸发得慢。对于平坦空间中的施瓦西黑洞和赖斯纳-诺德斯特姆黑洞，当黑洞的初始温度高于环境温度时，黑洞完全蒸发，霍金辐射最终被净化。对于 Schwarzschild-AdS 黑洞，当环境温度低于临界温度时，它会完全蒸发并净化霍金辐射。否则，它将与环境达到平衡状态，辐射最大程度地与黑洞纠缠在一起。我们的研究结果表明，黑洞的最终状态由环境温度和时间演化决定，以霍金辐射页面曲线为特征的信息净化过程的速度也受热环境显着影响。