The grand challenges of contemporary fundamental physics—dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem—all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress. This write-up is an initiative taken within the framework of the European Action on ‘Black holes, Gravitational waves and Fundamental Physics’.

We derive a closed-form expression of the orbit of Minkowski spacetime under arbitrary DiffpS 2 q super-Lorentz transformations and supertranslations. Such vacua are labelled by the superboost, superrotation and supertranslation fields. Impulsive transitions among vacua are related to the refraction memory effect and the displacement memory effect. A phase space is defined whose asymptotic symmetry group consists of arbitrary DiffpS 2 q super-Lorentz transformations and supertranslations. It requires a renormalization of the symplectic structure. We show that our final surface charge expressions are consistent with the leading and subleading soft graviton theorems. We contrast the leading BMS triangle structure to the mixed overleading/subleading BMS square structure. 1

The symmetry algebra of asymptotically flat spacetimes at null infinity in three dimensions is the semi-direct sum of the infinitesimal diffeomorphisms on the circle with an abelian ideal of supertranslations. The associated charge algebra is shown to admit a non trivial classical central extension of Virasoro type closely related to that of the anti-de Sitter case.

ABSTRACT. Surface charges and their algebra in interacting Lagrangian gauge field theories are constructed out of the underlying linearized theory using techniques from the variational calculus. In the case of exact solutions and symmetries, the surface charges are interpreted as a Pfaff system. Integrability is governed by Frobenius' theorem and the charges associated with the derived symmetry algebra are shown to vanish. Surfaces charges reproduce well-known Hamiltonian and covariant phase space expressions. In the asymptotic context, we provide a generalized covariant derivation of the result that the representation of the asymptotic symmetry algebra through charges may be centrally extended. Comparision with Hamiltonian and covariant phase space methods are done in appendix.

We describe a new class of boundary conditions for AdS d+1 under which the boundary metric becomes a dynamical field. The key technical point is to show that contributions from boundary counter-terms in the bulk gravitational action render such fluctuations normalizable. In the context of AdS/CFT, the analogue of Neumann boundary conditions for AdS promotes the CFT metric to a dynamical field but adds no explicit gravitational dynamics; the gravitational dynamics is just that induced by the conformal fields. Other AdS boundary conditions couple the CFT to a gravity theory of choice. We use this correspondence to briefly explore the coupled CFT + gravity theories and, in particular, for d = 3 we show that coupling topologically massive gravity to a large N CFT preserves the perturbative stability of the theory with negative (3-dimensional) Newton's constant.Here (Dg) g (0) is the measure which integrates over all metrics g ij corresponding via (1.2), (1.3) to the given boundary metric g (0)ij . The "Dirichlet" action S Dir = S EH + S GH + S ct contains the usual bulk Einstein-Hilbert and cosmological constant terms (S EH ) as well as the Gibbons-Hawking boundary term (S GH ) and the counter-terms [17,18,19,20] (S ct ) at infinity required to make the action a well-defined variational principle for each fixed 1 We shall treat the correspondence as a duality between a theory on AdS d+1 and a d-dimensional CFT.We assume that any extra compact factor K in the spacetime (e.g., S 5 , or S 3 × T 4 ) has been dealt with by Kaluza-Klein reduction; i.e. by expressing the 10-or 11-dimensional fields as sums of harmonics on K. We refer only to the resulting (d + 1)-dimensional metric in (1.2).

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We present a first-principles derivation of the main results of the Kerr/CFT correspondence and its extensions using only tools from gravity and quantum field theory, filling a few gaps in the literature when necessary. Firstly, we review properties of extremal black holes that imply, according to semi-classical quantization rules, that their near-horizon quantum states form a centrally-extended representation of the one-dimensional conformal group. This motivates the conjecture that the extremal Kerr and Reissner-Nordström black holes are dual to the chiral limit of a two-dimensional CFT. We also motivate the existence of an SL(2, ℤ) family of two-dimensional CFTs, which describe in their chiral limit the extremal Kerr-Newman black hole. We present generalizations in anti-de Sitter spacetime and discuss other matter-coupling and higher-derivative corrections. Secondly, we show how a near-chiral limit of these CFTs reproduces the dynamics of near-superradiant probes around near-extremal black holes in the semi-classical limit. Thirdly, we review how the hidden conformal symmetries of asymptotically-flat black holes away from extremality, combined with their properties at extremality, allow for a microscopic accounting of the entropy of non-extremal asymptotically-flat rotating or charged black holes. We conclude with a list of open problems.