Final Activity Report Summary - HIDIMBHS (Black holes in higher dimensional gravity theories) It is often the case that an analogue model description of a given theory provides insightful clues to our understanding of it. A well-known example is the charged liquid drop model for the nuclei developed for the mechanism of nuclear fission by Niels Bohr and John Wheeler. During this project we introduced and explored an analogy between higher dimensional black holes and liquid drops. We also studied the connection between the Gregory-Laflamme instability, that afflicts extended black holes, like black strings and black membranes, and a hydrodynamical instability that makes long fluid cylinders break (this is the mechanism responsible for the break of water jet in a faucet and for the formation of water droplets in rain). One of the biggest advances of last decade in gravitational physics was the realisation that there is a duality between some gravity and quantum field theories (the AdS/CFT duality). Moreover, in the last two years it was found that in the high energy density limit, quantum field theories have a hydrodynamical description. Combined, these two results imply that gravity has a hydrodynamical description (in a certain regime)! The old suggestive observation that black holes often resemble lumps of fluid is then taken beyond the level of an analogy to a precise duality. In a series of works done during this MC project, we investigated aspects of this duality. We clarified the relation between area minimisation of the fluid vs. area maximisation of the black hole horizon, and the connection between surface tension and curvature of the fluid, and surface gravity of the black hole. We studied some hydrodynamic instabilities in fluids and identified the dual instabilities in the associated black holes. We used the rich phase diagram of fluid solutions to identify and predict new black hole solutions and we used our fluid results to discuss many unknown features of gravitational systems. Black holes have an entropy proportional to their horizon area. One of the most intriguing puzzles of black hole thermodynamics is connected with the identification of the individual microstate geometries that, after a statistical average, should yield the macroscopic black hole entropy. The so-called 'fuzzball proposal' introduced a way to identify these microscopic geometries. For supersymmetric black holes, this proposal had encouraging success. However, if the fuzzball proposal is to be useful, it must also be extended to non-supersymmetric systems that are the rule rather the exception at low energies. We discovered that non-supersymmetric microstate geometries are afflicted by the so-called ergoregion instability. Therefore, according to the proposal, one might expect that the associated black hole should be also unstable. However, in this project we found they are not! This posed challenges to the proposal that are being addressed in the recent years. One of the interesting achievements of string theory has been the microscopic or statistical description of thermal Hawking radiation of a black hole. Hawking radiation is usually entangled with superradiant emmission phenomena (superradiance is the process whereby a incident wave gets amplified when scatters a rotating black hole; in the presence of a reflecting wall, the multiple amplification / reflection leads to a superradiant instability). We found that superradiance also has a clear microscopic description: it can be understood in terms of collisions of fermionic string excitations (obeying Fermi-Dirac statistics and carrying the spin essential for the superradiant process) on the D-branes that constitute microscopically the black hole. TeV-scale gravity scenarios propose that extra dimensions might be realized already at low energies, if the higher-dimensional fundamental Planck mass is of the order or the electroweak scale. If so, LHC at CERN might find evidence for the existence of extra compact dimensions and for black hole production. In this project, we found the analytical solution (in the perturbative small mass regime) that describes an array of black holes of different sizes living in extra compact dimensions.