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We analyse different classical formulations of General Relativity in the Batalin (Frad-
kin) Vilkovisky framework with boundary, as a first step in the program of CMR [1] quantisation. Success and failure in satisfying the axioms will allow us to discriminate among the different descriptions, suggesting that some are more suitable than others in view of perturbative quantisation. Based on a joint work with A. Cattaneo [2, 3] we will present the details of the application of the BV-BFV formalism to the Einstein-Hilbert and Palatini-Holst formulations of General Relativity. We show that the two descriptions are no longer equivalent from this point of view, and we discuss possible interpretations of this result.

[1] A. S. Cattaneo, P. Mnëv, N. Reshetikhin, Classical BV theories on manifolds with boundary, Comm. Math. Phys. 332, 2, 535-603 (2014); A.S. Cattaneo, P. Mnëv, N. Reshetikhin, Perturbative quantum gauge theories on manifolds with boundary, arXiv:1507.01221
[2] A. S. Cattaneo, M. Schiavina, BV-BFV analysis of General Relativity. Part I: Einstein Hilbert action, arXiv:1509.05762 (2015).
[3] A. S. Cattaneo, M. Schiavina, BV-BFV analysis of General Relativity. Part II: Palatini Holst action, in preparation; A. S. Cattaneo, M. Schiavina, On time, in preparation.

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. Typically these equations can only be solved numerically, but they become amenable to analytic solution in the extremal limit when the black hole achieves maximal angular momentum and an infinite-dimensional conformal symmetry emerges in the high-redshift region near its horizon. This constitutes an example of critical behavior in astronomy. We use the near-horizon scaling symmetry of the extreme Kerr metric to determine universal properties of physics near rapidly spinning black holes.

Advanced LIGO has recently started operating, with the promise that discoveries of gravitational wave transients will begin within in the next few years. As astrophysical observatories, LIGO and similar experiments may inform our knowledge of a variety of topics, including heavy element formation, dynamical capture of black holes, and the neutron star equation of state. In this talk, I will highlight recent efforts to quickly identify and distribute transients found with LIGO, and explore some of the astrophysics questions we hope to address.

The Hartle-Hawking (HH) no-boundary proposal provides a Euclidean path integral prescription for a measure on the space of all possible initial conditions. Apart from  saddle point  and  minisuper-space calculations, it is hard to obtain results using the unregulated path integral. A promising choice of spacetime  regularisation comes from the causal set (CST) approach to quantum gravity.  Using analytic results as well as Markov Chain Monte Carlo and numerical integration methods we obtain  the HH wave function in a theory of non-perturbative 2d CST. We find that the  wave function is sharply peaked with the peak geometry changing discretely with "temperature". In the low temperature regime the peak corresponds to causal sets which have no continuum counterpart but exhibit physically interesting behaviour. They show a rapid spatial expansion with respect to the discrete proper time as well as  a high degree of spatial homogeneity due to extensive overlap of the causal past. While our results are limited to 2 dimensions they provide a concrete example of how quantum gravity could explain the initial conditions for our observable universe.

In this talk I will describe numerical constructions of gravitational
duals of theories deformed by localized Dirac delta sources for scalar
operators. We perform two different constructions, one at zero and
the other at nonzero temperature. Surprisingly we find that imposing the preservation of scale
invariance at zero temperature requires the bulk scalar self-interaction potential to be
the one found in a certain Kaluza-Klein compactification of 11D supergravity.
The gravitational setup seems a-priori to be quite unusual and challenging
from the numerical relativity perspective.

Using holography, we study the evolution of a spatially homogeneous, far from equilibrium, strongly coupled N=4 supersymmetric Yang-Mills plasma with a non-zero charge density or a background magnetic field. This gauge theory problem corresponds, in the dual gravity description, to an initial value problem in Einstein-Maxwell theory with homogeneous but anisotropic initial conditions. We explore the dependence of the equilibration process on different aspects of the initial departure from equilibrium and, while controlling for these dependencies, examine how the equilibration dynamics are affected by the presence of a non-vanishing charge density or an external magnetic field. The equilibration dynamics are remarkably insensitive to the addition of even large chemical potentials or magnetic fields, the equilibration time is set primarily by the form of the initial departure from equilibrium. For initial deviations from equilibrium which are well localized in scale, we formulate a simple model for equilibration times which agrees quite well with our results.