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arXiv 2206.04410gr-qc
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Einstein引力中毛状黑洞的弱宇宙审查猜想

Weak Cosmic Censorship Conjecture of Hairy Black Holes in Einstein Gravity

Aofei Sang, Jie Jiang

摘要:

除了Kerr-Newman黑洞外,广义相对论中的多毛黑洞在引力和宇宙学中也得到了广泛的研究。本文推广Sorce-Wald方法,在不使用物质场的度规和拉格朗日量的情况下,证明了Einstein引力场中静态球对称多毛黑洞的弱宇宙监督猜想(WCCC).我们研究的WCCC在碰撞过程中,而不需要球对称的扰动物质场。在假定时空稳定性条件的基础上,将高斯零坐标应用于变分恒等式,导出了反映物质场零能量条件的前两阶微扰不等式.结果表明,在二级近似下,上述扰动过程不能破坏近极值静态多毛黑洞。我们的结果表明,只要在微扰水平下物质场满足零能条件,WCCC对于Einstein引力下的毛状黑洞是普适的。

英文摘要:

Apart from the Kerr-Newman black holes, the hairy black holes in general relativity have been widely investigated in the gravity and cosmology. In this paper, we extend the Sorce-Wald method to prove the weak cosmic censorship conjecture (WCCC) of the static and spherically symmetric hairy black holes in the Einstein gravity without using the explicit expressions of the metric and lagrangian for matter fields. We examine the WCCC in the collision process without requiring the spherically symmetry of the perturbation matter fields. After assuming the stability condition of spacetime and applying the Gaussian null coordinates into the variational identities, we derive the first two order perturbation inequalities which reflects the null energy condition of the matter fields. As a result, we find that nearly extremal static hairy black hole cannot be destroyed in the above perturbation process under the second-order approximation. Our result implies that the valid of the WCCC is universal for the hairy black hole in the Einstein gravity as long as the matter fields satisfy the null energy condition under the perturbation level.

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