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.
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.
The talk will summarize some results relating to clarifying the physical significance of the characteristic structure of the Weyl curvature tensor, and proposals for its utilization. I will begin by showing how null force-free or vacuum electrodynamic solutions experience reduced scattering by propagating along the principal null directions (GPNDs) of the spacetime, as if they were the flatter directions of the curvature tensor.
In the last few years the possibility of constraining dark matter with astrophysical observations of compact objects, such as white dwarfs, neutron stars and black holes, has been explored. The ultra-high density interior of neutron stars and the strong-curvature regions near massive black holes make these objects unique laboratories to test weakly-interacting particles.
We argue that the infinite-dimensional BMS symmetry discovered by Bondi et. al in the 60s provides an exact symmetry of the quantum gravity S-matrix. The Ward identity of this symmetry is shown to be precisely Weinberg's soft graviton theorem, also discovered in the 60s. A parallel infinite-dimensional symmetry is found to be generated in nonabelian gauge theories by gauge transformations which go to an angle-dependent finite constant at null infinity. The Ward identity of this symmetry is shown to be the soft gluon theorem.
Horava's proposal to use Lifshitz propagators for gravitons above certain energy scales may provide a viable theory of quantum gravity without further need of UV completion. In my talk, I will address the question of whether the complete lack of Lorentz invariance above a certain energy scale is a big problem for any realistic construction. I will argue that it is not, provided that the onset of Lifshitz scaling for gravitons occurs at momentum scale much lower than the Planck mass.