On the dynamics and stability of rotating higher dimensional black holes

We study the stability of fast-spinning D=5 black rings making use of the blackfold formalism. We also construct a new effective theory involving blackfolds with transverse spins, able to describe rotating higher dimensional black holes with a set of finite angular momenta. The blackfold approach is a perturbative formalism that allows to capture the behaviour of higher dimensional black holes with high angular momenta. We use it to discuss the dynamic instabilities of boosted black strings, obtaining the expressions for longitudinal and elastic quasinormal modes up to contributions proportional to the square of the horizon scale. A longitudinal Gregory-Laflamme instability is found, as expected. We also study the instabilities of black rings, and we compute the quasinormal frequencies for high mode numbers m= k R and up to contributions proportional to the horizon scale. They agree with the corresponding large-D frequencies, and they signal the presence of a Gregory-Laflamme instability. Finally, we construct a new effective theory describing blackfolds with transverse angular momenta, considering explicitly Kerr black strings, doubly-spinning Myers-Perry black strings and black ring strings. We use these results to build six-dimensional solutions with horizon topology consisting in the product of 2-spheres with 2-tori, and black ring p-balls with even p, endowed with horizon geometry S^2 x S^1 x B^p. The range of validity of our calculation includes relatively low reduced transverse momenta, down to j ∼ 0.1, considerably improving the original blackfold description of a large class of configurations. Finally, as an example, we analyse the leading order stability of black ring p-branes and of D=5 Myers-Perry black branes. In both cases, any accessible configuration turns out to be unstable.