This series consists of talks in areas where gravity is the main driver behind interesting or peculiar phenomena, from astrophysics to gravity in higher dimensions.
One version of the membrane paradigm states that as far as outside observers are concerned, black holes can be replaced by a dissipative membrane with simple physical properties located at the stretched horizon. We demonstrate that such a membrane paradigm is incomplete in several aspects. We argue that it generically fails to capture the massive quasinormal modes, unless we replace the stretched horizon by the exact event horizon, and illustrate this with a scalar field in a BTZ black hole background.
A prime challenge to our understanding of galaxy formation concerns the scarcity of dwarf galaxies compared with the numerous low-mass halos expected in the current ΛCDM paradigm. This is usually accounted for by assuming that energetic feedback from evolving stars confines dwarf galaxy formation to relatively massive halos spanning a narrow mass range. I will highlight a number of observations that may be used to test this assumption and discuss the puzzles and challenges that arise from this analysis.
In the context of gauge/gravity duality, it has been suggested that the far-from equilibrium strongly coupled dynamics encountered in ultrarelativistic heavy-ion collisions may be modelled as the collisions of black holes in asymptotic anti-de-Sitter spacetimes. I will present results from the evolution of spacetimes that describe the merger of asymptotically global AdS black holes in 5D with an SO(3) symmetry. The initial trapped regions are sourced by scalar field collapse and we are able to evolve through the ensuing black hole merger as well as subsequent ring-down.
There are about nine astrophysical black holes with measurements of the black hole's spin via the continuum fitting method. Several of these black holes drive powerful jets, which appear to extract the black hole's rotational energy. I will discuss the theory behind these observations, with a particular focus on the black hole membrane paradigm. The membrane paradigm is useful on a practical level for understanding black hole jets. However, it may also be related to fundamental physics through holography and AdS/CFT.
General relativity enjoys phenomenal success in agreeing with experiments and observations, but it must break down at some point. Astrophysics can give guidance for what type of theory may correct general relativity, if we know which phenomenology to look for. I will discuss the possible corrections to the structure of compact objects, the binary problem, and observations with pulsar timing and gravitational wave detection.
Plasma-filled magnetospheres can extract energy from a spinning black hole and provide the power source for a variety of observed astrophysical phenomena. These magnetospheres are described by the highly nonlinear equations of force-free electrodynamics, or FFE. Typically these equations can only be solved numerically. In this talk I will explain how to analytically obtain several infinite families of exact solutions of the full nonlinear FFE equations very near the horizon of a maximally spinning black hole, where the energy extraction takes place.
Recent numerical simulations  have suggested that two dimensional superfluid turbulence is characterized by a direct cascade of energy to small length scales, in contrast to the inverse cascade of normal fluids, where energy is transported to large length scales. This direct cascade is characterized by many vortex-antivortex annihilation events. Recent experimental work  on Bose-Einstein condensates appears to demonstrate qualitatively similar physics.
Astronomical observation suggests the existence of near-extreme Kerr black holes whose horizons spin at nearly the speed of light. Properties of diffeomorphisms imply that the dynamics of the high-redshift near-horizon region of near-extreme Kerr, which includes the innermost-stable-circular-orbit (ISCO), is governed by an infinite-dimensional emergent conformal symmetry. This symmetry may be exploited to analytically, rather than numerically, compute a variety of potentially observable processes.
Our current definition of what a black hole is relies heavily on the assumption that there exists a finite maximum speed of propagation for any signal. Indeed, one is tempted to think that the notion of a black hole has no place in a world with infinitely fast signal propagation. I will use concrete examples from Lorentz-violating gravity theories to demonstrate that this naive expectation is not necessarily true.
A geometric inequality in General Relativity relates quantities that have both a physical interpretation and a geometrical definition. It is well known that the parameters that characterize the Kerr-Newman black hole (angular momentum, charge, mass and horizon area) satisfy several important geometric inequalities. Remarkably enough, some of these inequalities also hold for dynamical black holes. This kind of inequalities, which are valid in the dynamical and strong field regime, play an important role in the characterization of the gravitational collapse.