Instabilities of extremal rotating black holes in higher dimensions

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摘要：

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

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关键词：

High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics

DOI：

10.1007/s00220-015-2410-0

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年份：

2014