Near horizon physics for Kerr black holes

One of the biggest challenges of modern theoretical physics is to merge its two pillars, general relativity and quantum mechanics, into a unified theory of quantum gravity. In that context, black holes are deeply interesting objects as they are pointing towards the incompleteness of our modern understanding of the gravitational interaction, Einsteins general relativity. The problem is far from being only an academic one, since black holes of various types are believed to populate our universe. The research projet Near horizon physics for Kerr black holes aims to study aspects of astrophysical black holes from the point of view of an observer at the horizon, and by that, to improve our comprehension of quantum gravity. Classically, black holes are characterised by three numbers: their mass, angular momentum and electric charge. This fact is often paraphrased as "black holes have no hair". Nevertheless, it has been recently found that three dimensional black hole horizons could be dressed with soft hair, which is made of zero energy excitations. Soft hair has played, and is expected to play, an important role in various issues in black hole physics. The goal of this research project is to develop the soft hair physics for Kerr black holes. More precisely, we plan to build a consistent set of boundary conditions at the horizon for Kerr black holes, allowing for soft hair. Furthermore, we will study the relations between measures made by observers located in the asymptotic and the near horizon region. Then, we plan to identify the microstates, in the same way as the three dimensional case. Another aspect of the project is to consider dynamical processes, like absorption and emission of semi- classical black holes and to answer whether or not, information of falling matter in a black hole could be stored in its soft hair.

The goal of this Lise-Meitner project was to describe black hole physics from the point of view of an observer located at the horizon. We were interested in particular in Kerr black holes and phenomena such as black hole evaporation or matter falling into the black hole. Tackling this requires mathematically to characterize the black hole horizon that can have some non trivial flux passing through. This is encoded in leaky boundary conditions that we displayed. We also considered the symmetries of such boundary conditions and discussed what was the maximal symmetry algebra. This tells how much information is needed to describe one solution in the classical phase space. This also provides the organizational structure of the phase space. In particular we related the physical situation when no physical flux is passing through that surface to a specific mathematical property, namely the integrability of generators associated to such symmetries. We finally revealed a horizon memory effect encoding gravitational waves passing through the black hole horizon. Overall this project has largely yielded significant progress in the description of the classical phase space of gravity when leakyness is allowed.