Final Report Summary - LIMITSOFGR-2011-TPS (The limits of general relativity) General Relativity (GR) has had outstanding success as a gravitation theory for almost a century now. However, it does not incorporate quantum effects, which are expected to become very important in certain regimes, such as the early universe or the vicinity of black holes. This signals the need for a more fundamental gravity theory, dubbed ``quantum gravity'', which will bridge the gap between GR and Quantum Field Theory. Most contemporary attempts towards establishing such a theory seem to agree on one issue: that corrections with respect to GR will arise.On the other hand, current observations indicate that phenomenology usually related with gravity goes beyond the predictions of GR if only ordinary matter is taken into account, typical examples being the accelerated expansion of the universe or the rotation curves of galaxies. Even though these unexpected phenomena can be attributed to some unknown energy components of the universe, referred to as dark matter and dark energy, the obscure and mysterious nature of the latter calls for an explanation. Clearly, the very existence of dark matter and dark energy is inferred by their effect on gravitational dynamics. As such it could possibly be attributed to our poor understanding of the gravitational interaction at scales larger than that of the Solar system.The combination of the theoretical and the experimental evidence mentioned above seems to indicate that GR does not tell us the whole story about gravity. Indeed the latter appears to be the most enigmatic interaction in nature nowadays and the two problems just mentioned are among the most important questions in theoretical physics and cosmology. It seems quite clear that understanding the puzzles of gravity beyond GR is an essential step in order to understand the cosmos and achieve longstanding goals likes the unification of all interactions. The main objective of this project is to study and understand the limitations of GR through a synthetic approach: i) By studying candidate theories or models which can provide insight into a quantum gravity theory, ii) by analyzing classical alternatives to GR, and iii) by exploring regimes where gravity is not yet fully understood (even in GR). The first is crucial as it provides the fundamental motivation for any deviation from GR. The second is instrumental in making contact with infrared phenomenology and for studying the effects of deviation from GR in cosmology and astrophysics. As for the third, it suffices to say that systems where gravity it strong, such as black holes and compact stars, are natural laboratories for the gravitational interaction. To this end, an extended research group has been gradually put together, consisting (on September 31st 2013) of 2 PhD students, 4 Postdoctoral Research Associates, and the PI. This group has been active in all 3 of the the aforementioned areas. In the first 18 months our results have already led to 13 publication (2 more currently under review) in peer-reviewed international journals, and 3 publications in peer-reviewed conference proceedings. Some of the main results obtained in this period are listed below:- Lorentz violating models of quantum gravity have been studied, both theoretically and phenomenologically. On the theoretical front, a new and interesting variant of such models has been proposed. On the phenomenological front, astronomical observations have been used to impose a novel and very strong constraint on fairly generic theories of this type. - Black holes in theories of Lorentz violations have been extensively studied. Rotating black hole solutions have been obtained. These studies have provided new insight into the causal structure of black holes in the presence of Lorentz violations and raised important new questions.- Gravitation theories whose action contain auxiliary field have been considered. A new, very efficient parametrisation has been introduced for these theories. This has allowed us to demonstrate that they generically lead to very violent changes of the gravitational field whenever there are rapid changes in the matter density. This phenomenologically unacceptable behaviour leads to unprecedented constraints on these theories.- It has been shown that black holes surrounded by matter could actually develop scalar hair, unlike what was believed previously. This can have important astrophysical consequences. In particular, if these scalar hair were to be detected, they would reveal the presence of a scalar field as a (co-)mediator of the gravitational interaction. This in turn would imply that General Relativity need to be extended. This results has also received significant attention from popular science journals, newspaper columns, and blogs.- Significant advances have been made in understanding the role of self-force in particle trajectories around black holes. The self force has been calculated for the first time for eccentric orbits and for spacetimes that are not asymptotically flat. The role of the self force in attempts to violate the cosmic censorship conjecture by shooting particles into black holes has also been considered.- The gradient expansion technique has been developed for generalised scalar-tensor theories of gravity. This is a useful tool for early universe cosmology and studies on non-gaussianity in cosmological perturbations (which in turn can be a smoking gun observation for such theories).- A new class of ghost-free massive gravity models has been proposed.The group was very efficient in disseminating these results. Its members have already given more than 25 seminars and presentations at other institutes, conferences, and workshops. Approximately half of these talks were invited talks. Additionally, a visitor program was established and in the period April 2012 -September 2013 we had more than 15 scientist from other institutions visiting our group (taking advantage of alternative sources of funding as well). Finally, members of our group have participated in the organisation of 2 workshops and 1 conference: the "Kavli IPMU focus week on Gravity and Lorentz violations" workshop, held in February 2013 at Tokyo, Japan, the "Strong gravity beyond GR" workshop, held in March 2013 in Lisbon, Portugal, and the "2nd Mediterranean Conference on Classical and Quantum Gravity", held in June 2013 at Veli Losinj, Croatia.18 months after the starting date of the project the PI and the group decided to gradually move to the University of Nottingham. As a result the project (as a funded Marie Curie Career Integration Grant) had to be interrupted. The project was at that stage within, if not ahead of, schedule in what regards its objectives.