The existence of Chandrasekhar’s limit has played various decisive roles in astronomical observations for many decades. However, various recent theoretical investigations suggest that gravitational collapse of white dwarfs is withheld for arbitrarily high masses beyond Chandrasekhar’s limit if the equation of state incorporates the effect of quantum gravity via the generalized uncertainty principle. There have been a few attempts to restore the Chandrasekhar limit but they are found to be inadequate. In this paper, we rigorously resolve this problem by analysing the dynamical instability in general relativity. We confirm the existence of Chandrasekhar’s limit as well as stable mass–radius curves that behave consistently with astronomical observations. Moreover, this stability analysis suggests gravitational collapse beyond the Chandrasekhar limit signifying the possibility of compact objects denser than white dwarfs.

几十年来，钱德拉塞卡极限的存在在天文观测中发挥了各种决定性作用。然而，最近的各种理论研究表明，如果状态方程通过广义不确定性原理纳入了量子引力的效应，那么对于超出钱德拉塞卡极限的任意高质量，白矮星的引力坍缩就会被抑制。人们曾多次尝试恢复钱德拉塞卡极限，但结果发现这些努力都是不够的。在本文中，我们通过分析广义相对论中的动力学不稳定性来严格解决这个问题。我们证实了钱德拉塞卡极限的存在以及与天文观测一致的稳定质量半径曲线。此外，这种稳定性分析表明，引力塌缩超出了钱德拉塞卡极限，这意味着致密天体可能比白矮星密度更大。