Cosmic censorship and the evolution of d-dimensional charged evaporating black holes

Cosmic censorship and the evolution of d-dimensional charged evaporating black holes

The cosmic censorship conjecture essentially states that naked singularities should not form from \emph{generic} initial conditions. Since black hole parameters can change their values under Hawking evaporation, one has to ask whether it is possible to reach extremality by simply waiting for the black hole to evaporate. If so a slight perturbation would likely render the singularity naked. Fortunately, at least for the case of asymptotically flat 4-dimensional Reissner-Nordstr\"om black hole, Hiscock and Weems showed that it can never reach extremality despite the fact that for a sufficiently massive black hole, its charge-to-mass ratio can increase during Hawking evaporation. Hence cosmic censorship is never violated by Hawking emission. However, we know that under some processes, it is easier to violate cosmic censorship in higher dimensions, therefore it is crucial to generalize Hiscock and Weems model to dimensions above four to check cosmic censorship. We found that Hawking evaporation cannot lead to violation of cosmic censorship even in higher dimensional Reissner-Nordstr\"om spacetimes. Morerover, it seems to be more difficult to reach extremality as number of dimension increases.

宇宙监督猜想本质上表明，裸奇点不应从一般初始条件形成。由于黑洞参数在霍金蒸发过程中会改变其值，人们不得不问，是否仅仅通过等待黑洞蒸发就有可能达到极端状态。如果是这样，轻微的扰动可能会使奇点裸露。幸运的是，至少对于渐近平直的4维赖斯纳 - 诺德斯特龙黑洞的情况，希斯科克和威姆斯表明，尽管对于一个足够大质量的黑洞，其荷质比在霍金蒸发过程中会增加，但它永远无法达到极端状态。因此，霍金辐射永远不会违反宇宙监督。然而，我们知道在某些过程中，在更高维度更容易违反宇宙监督，因此将希斯科克和威姆斯的模型推广到四维以上以检验宇宙监督是至关重要的。我们发现，即使在更高维的赖斯纳 - 诺德斯特龙时空里，霍金蒸发也不会导致违反宇宙监督。而且，随着维度数量的增加，似乎更难达到极端状态。