Black holes in anti-de Sitter (AdS) backgrounds play a pivotal role in the gauge/gravity duality where they determine, among other things, the approach to equilibrium of the dual field theory. We undertake a detailed analysis of perturbed Kerr-AdS black holes in four-and five-dimensional spacetimes, including the computation of its quasinormal modes, hydrodynamic modes and superradiantly unstable modes. Our results shed light on the possibility of new black hole phases with a single Killing field, possible new holographic phenomena and phases in the presence of a rotating chemical potential, and close a crucial gap in our understanding of linearized perturbations of black holes in anti-de Sitter scenarios.

Ultralight bosons and axion-like particles appear naturally in different scenarios and could solve some long-standing puzzles. Their detection is challenging, and all direct methods hinge on unknown couplings to the Standard Model of particle physics. However, the universal coupling to gravity provides model-independent signatures for these fields. We explore here the superradiant instability of spinning black holes triggered in the presence of such fields. The instability taps angular momentum from and limits the maximum spin of astrophysical black holes. We compute, for the first time, the spectrum of the most unstable modes of a massive vector (Proca) field for generic black-hole spin and Proca mass. The observed stability of the inner disk of stellar-mass black holes can be used to derive direct constraints on the mass of dark photons in the mass range 10 −13 eV m V 3 × 10 −12 eV. By including also higher azimuthal modes, similar constraints apply to axion-like particles in the mass range 6 × 10 −13 eV m ALP 10 −11 eV. Likewise, mass and spin distributions of supermassive BHs -as measured through continuum fitting, Kα iron line, or with the future space-based gravitational-wave detector LISA -imply indirect bounds in the mass range approximately 10 −19 eV m V , m ALP 10 −13 eV, for both axion-like particles and dark photons. Overall, superradiance allows to explore a region of approximately 8 orders of magnitude in the mass of ultralight bosons.

We study the main properties of general linear perturbations of rotating black holes in asymptotically flat higher-dimensional spacetimes. In particular, we determine the quasinormal mode (QNM) spectrum of singly spinning and equal angular momenta Myers-Perry black holes (MP BHs). Emphasis is also given to the timescale of the ultraspinning and bar-mode instabilities in these two families of MP BHs. For the bar-mode instabilities in the singly spinning MP BH, we find excellent agreement with our linear analysis and the non-linear time evolution of Shibata and Yoshino for d = 6, 7 spacetime dimensions. We find that d = 5 singly spinning BHs are linearly stable. In the context of studying general relativity in the large dimension limit, we obtain the QNM spectrum of Schwarzschild BHs and rotating MP BHs for large dimensions. We identify two classes of modes. For large dimensions, we find that in the limit of zero rotation, unstable modes of the MP BHs connect to a class of Schwarzschild QNMs that saturate to finite values.

Solutions corresponding to finite temperature (anti)-D3 and M2 branes localised in flux backgrounds are constructed in a linear approximation. The flux backgrounds considered are toy models for the IR of the Klebanov-Strassler solution and its M-theory analogue, the Cvetič-Gibbons-Lü-Pope solution. Smooth solutions exist for either sign charge, in stark contrast with the previously considered case of smeared black branes. That the singularities of the anti-branes in the zero temperature extremal limit can be shielded behind a finite temperature horizon indicates that the singularities are physical and resolvable by string theory. As the charge of the branes grows large and negative, the flux at the horizon increases without bound and diverges in the extremal limit, which suggests a resolution via brane polarisationà la Polchinski-Strassler. It therefore appears that the anti-brane singularities do not indicate a problem with the SUSY-breaking metastable states corresponding to expanded anti-brane configurations in these backgrounds, nor with the use of these states in constructing the de Sitter landscape.

We obtain finite-temperature M2 black branes in 11-dimensional supergravity, in a $G_4$-flux background whose self-dual part approaches a solution of Cveti\v{c}, Gibbons, L\"u, and Pope, based upon Stenzel's family of Ricci-flat K\"ahler deformed cones. Our solutions are asymptotically $AdS_4$ times a 7-dimensional Stiefel manifold $V_{5,2}$, and the branes are ``smeared'' to retain $SO(5)$ symmetry in the internal space. The solutions represent a mass deformation of the corresponding dual $CFT_3$, whose full description is at this time only partially-understood. We investigate the possibility of a confinement/de-confinement phase transition analogous to the $AdS_5 \times S^5$ case, and a possible Gregory-Laflamme type instability which could lead to polarised brane solutions which break $SO(5)$. We discuss possible consequences for AdS/CFT and the KKLT cosmological uplift mechanism.Comment: 33 pages, 3 figure