Holography in out of equilibrium systems and asymptotic symmetries of black holes

This thesis, presented in the form of a "compilation of articles", touches different areas of Theoretical Physics.

The first part, which comprises the first two articles, focuses on using applied holography to study out-of-equilibrium physics. More specifically, in the first article we study quantum processes called quenches and we show, by holographically constructing gravitational dual backgrounds, the way to implement a quantum quench with a real change in the hamiltonian in a Lorentz-invariant manner. The second article is framed under the theory of anomalous transport. The object of study is the gravitational contribution to the chiral anomaly, which through the chiral magnetic effect induces an energy current proportional to the square of the temperature when the system is in equilibrium. In this framework, we implement holographic quantum quenches to bring the system out of equilibrium, where no temperature can be well defined. Our results indicate a strong suppression of this effect when the system is very far from equilibrium.

The second part of the thesis lies in the context of exact, non-linear general relativity.

In the third article, we characterize generic, non-expanding black hole horizons and study the effect of supertranslations on them. We present a freely specifiable data set which is both necessary and sufficient to reconstruct the full horizon geometry and is composed of objects that are invariant under supertranslations. Therefore we conclude that these transformations do not transform the geometry of the horizon and should be regarded as pure gauge.