Perturbations and Stability of Higher-Dimensional Black Holes

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In this lecture, I explain the gauge-invariant formulation for perturbations of background spacetimes with untwisted homologous Einstein fibres, which include lots of practically important spacetimes such as static black holes, static black branes and rotating black holes in various dimensions. As applications, we discuss the stability of static black holes in higher dimensions and flat black branes.
45 pages, 9 figures. Based on the lecture given at the 4th Aegean Summer School. References added and typos corrected

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