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arXiv 1408.0801hep-thgr-qcmath-phmath.MP
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高维极端旋转黑洞的不稳定性

Instabilities of extremal rotating black holes in higher dimensions

Stefan Hollands, Akihiro Ishibashi

摘要:

最近,Durkee和Reall给出了$d\ge 4$维中旋转、极值、渐近闵可夫斯基黑洞(如Myers-Perry黑洞)线性不稳定性的一个判据.他们考虑了某个椭圆算子$\cA$,它作用于视界固有的对称无迹张量。部分基于数值证据,他们提出,如果该算子的最低本征值小于临界值$-1/4$(称为“有效BF-界限”),那么黑洞是线性不稳定的。在本文中,我们证明了他们的猜想的一个扩展版本。我们的证明使用的方法相结合,如(i)“正则能量法”的Hollands-Wald,(ii)代数特殊性质的近视界几何与黑洞,(iii)的Corvino Schoen技术,(iv)半经典分析。我们的证明方法也适用于旋转,极值渐近反deSitter黑洞。在这种情况下,我们发现了超自旋黑洞的额外不稳定性。虽然我们在本文中只明确讨论极值黑洞,我们认为我们的结果可以推广到{ \em near}极值黑洞。

英文摘要:

Recently, Durkee and Reall have conjectured a criterion for linear instability of rotating, extremal, asymptotically Minkowskian black holes in $d\ge 4$ dimensions, such as the Myers-Perry black holes. They considered a certain elliptic operator, $\cA$, acting on symmetric trace-free tensors intrinsic to the horizon. Based in part on numerical evidence, they suggested that if the lowest eigenvalue of this operator is less than the critical value $-1/4$ ( called "effective BF-bound"), then the black hole is linearly unstable. In this paper, we prove an extended version of their conjecture. Our proof uses a combination of methods such as (i) the "canonical energy method" of Hollands-Wald, (ii) algebraically special properties of the near horizon geometries associated with the black hole, (iii) the Corvino-Schoen technique, and (iv) semiclassical analysis. Our method of proof is also applicable to rotating, extremal asymptotically Anti-deSitter black holes. In that case, we find additional instabilities for ultra-spinning black holes. Although we explicitly discuss in this paper only extremal black holes, we argue that our results can be generalized to {\em near} extremal black holes.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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