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The surface charge algebra of generic asymptotically locally (A)dS4 spacetimes without matter is derived without assuming any boundary conditions. Surface charges associated with Weyl rescalings are vanishing while the boundary diffeomorphism charge algebra is non-trivially represented without central extension. The Λ-BMS4 charge algebra is obtained after specifying a boundary foliation and a boundary measure. The existence of the flat limit requires the addition of corner terms in the action and symplectic structure that are defined from the boundary foliation and measure. The flat limit then reproduces the BMS4 charge algebra of supertranslations and super-Lorentz transformations acting on asymptotically locally flat spacetimes. The BMS4 surface charges represent the BMS4 algebra without central extension at the corners of null infinity under the standard Dirac bracket, which implies that the BMS4 flux algebra admits no non-trivial central extension. [ABSTRACT FROM AUTHOR]

The aim of this paper is to give an overview to nonspecialists of recent arguments from fundamental physics in favor and disfavor of quantum corrections to black hole horizons. I will mainly discuss the black hole information paradox, its possible resolutions and shortly address its relevance or irrelevance to astronomy. [ABSTRACT FROM AUTHOR]

For this last lecture, we will focus on particular properties of astrophysically realistic 4d black holes, which are rotating and uncharged. We will concentrate on the stationary Kerr black hole solution which is the final state of collapse of matter. After reviewing its main features, we will study the maximally spinning limit of the Kerr solution, the extremal Kerr black hole. It is a very interesting solution because it admits near horizon limits with enhanced conformal symmetry. The limiting near-horizon geometries share features with anti-de Sitter spacetimes where holography and therefore quantum gravity is most understood. The attempts (with successes and failures) to describe the extremal Kerr black hole with holographic techniques is called the Kerr/CFT correspondence and will be briefly reviewed here. The final part of these lectures will be devoted to the analysis of gravitational perturbations around Kerr geometries. The Kerr black hole is currently under experimental tests by the LIGO/Virgo gravitational wave detectors. The final stages of black hole mergers consist in a quasi-normal mode ringing of the resulting black hole which is well-described by perturbation theory around the Kerr black hole. Since the Kerr black hole only depends upon two parameters, namely the mass and angular momentum, the resonance frequencies of the black hole are characteristic signatures of Einstein gravity. The emerging experimental science of black hole spectroscopy will soon test the limits of Einstein gravity and look for possible deviations. [ABSTRACT FROM AUTHOR]

General Relativity is a very complex theory whose quantization remains elusive. A reduced version of the theory exists: 3-dimensional Einstein's gravity to which this lecture is dedicated. As a toy-model, it is a very useful framework thanks to which we can experiment some techniques and derive features, some of which extend to the physical 4d case. In this lecture, we will review the typical properties of 3d gravity, which are mostly due to the vanishing of the Weyl curvature. Next we will turn to the AdS3 phase space: we will describe global features of AdS3 itself, give several elements on the Brown-Henneaux boundary conditions and the resulting asymptotic symmetry group, and finally discuss BTZ black holes. We will show that the asymptotically flat phase space can be obtained from the flat limit of the asymptotically AdS3 phase space. Finally, we will shortly present the Chern-Simons formulation of 3d gravity, which reduces the theory to the one of two non-abelian gauge vector fields. [ABSTRACT FROM AUTHOR]

For the next lecture, we consider four-dimensional asymptotically flat spacetimes, which are the solutions of General Relativity with localised energy-momentum sources. We will start with a review of the work of Penrose on the conformal compactification of asymptotically flat spacetimes in order to get a global view on the asymptotic structure. We will then concentrate on the properties of radiative fields by reviewing the work of van der Burg, Bondi, Metzner and Sachs of 1962. One may think at first that the group of asymptotic symmetries of radiative spacetimes is the Poincaré group, but a larger group appears, the BMSgroup which contains so-called supertranslations. Additional symmetries, known as superrotations, also play a role and we shall briefly discuss them too. Finally, we will give some comments on the scattering problem in General Relativity. We will show that the extended asymptotic group gives conserved quantities once junction conditions are fixed at spatial infinity [ABSTRACT FROM AUTHOR]

The main purpose of this first lecture is to introduce the concept of canonical surface charges in a generally covariant theory of gravity, whose General Relativity is the most famous representative. We will first show that a conserved stress tensor can be generated for any classical field theory. We will then motivate why we cannot define conserved currents and charges in Noether's fashion for generally covariant theories, and more globally, for theories that include gauge transformations. This will lead us to extend Noether's first theorem to formulate lower degree conservation laws, which will be exploitable for theories such as Einstein's gravity. On the way, we will discuss about the symplectic structure of abstract spaces of fields, and use the covariant phase space formalism to derive a powerful result linking this structure and the lower degree conserved forms. We will then be able to compute surface charges associated to these quantities and study their properties and their algebra. Along the text, some pedagogical examples will be provided, namely for pure Einstein's gravity, and Maxwells electrodynamics. Finally, we will present another possible definition of these surface charges and use the latter definition as an efficient tool to derive the conserved charges of Chern-Simons theory. [ABSTRACT FROM AUTHOR]

Near-maximally spinning black holes display conformal symmetry in their near-horizon region, which is therefore the locus of critical phenomena. In this paper, we revisit the Novikov–Thorne accretion thin disc model and find a new self-similar radiation-dominated solution in the extremely high spin regime. Motivated by the self-consistency of the model, we require that matter flows at the sound speed at the innermost stable circular orbit (ISCO).We observe that, when the disc pressure is dominated by radiation at the ISCO, which occurs for the best-fitting Novikov–Thorne model of GRS 1915+105, the Shakura–Sunyaev viscosity parameter can be expressed in terms of the spin, mass accretion rate and radiative efficiency. We quantitatively describe how the exact thin disc solution approaches the self-similar solution in the vicinity of the ISCO and for increasing spins. [ABSTRACT FROM AUTHOR]

The memory effect is a prediction of general relativity on the same footing as the existence of gravitational waves. The memory effect is understood at future null infinity as a transition induced by null radiation from a Poincaré vacuum to another vacuum. Those are related by a supertranslation, which is a fundamental symmetry of asymptotically flat spacetimes. In this paper, I argue that finite supertranslation diffeomorphisms should be extended into the bulk spacetime consistently with canonical charge conservation. It then leads to fascinating geometrical features of gravitational Poincaré vacua. I then argue that in the process of black hole merger or gravitational collapse, dramatic but computable memory effects occur. They lead to a final stationary metric which qualitatively deviates from the Schwarzschild metric. [ABSTRACT FROM AUTHOR]

We study three-dimensional consistent truncations of type IIB supergravity which admit warped AdS solutions. These theories contain subsectors that have no bulk dynamics. We show that the symplectic form for these theories, when restricted to the non-dynamical subsectors, equals the symplectic form for pure Einstein gravity in AdS. Consequently, for each consistent choice of boundary conditions in AdS, we can define a consistent phase space in warped AdS with identical conserved charges. This way, we easily obtain a Virasoro × Virasoro asymptotic symmetry algebra in warped AdS; two different types of Virasoro × Kač-Moody symmetries are also consistent alternatives. Next, we study the phase space of these theories when propagating modes are included. We show that, as long as one can define a conserved symplectic form without introducing instabilities, the Virasoro × Virasoro asymptotic symmetries can be extended to the entire (linearised) phase space. This implies that, at least at semi-classical level, consistent theories of gravity in warped AdS are described by a two-dimensional conformal field theory, as long as stability is not an issue. [ABSTRACT FROM AUTHOR]

We describe the most general asymptotically flat, stationary, non-extremal, dyonic black hole of the four-dimensional supergravity coupled to three vector multiplets that describes the low-energy regime of the STU model. Under U-dualities, this can be used as a seed to generate all single-centered stationary black holes of supergravity. The independent conserved charges are the mass, angular momentum, four electric charges and four magnetic charges; an independent NUT charge can also be added. Several aspects of the black hole are presented, including thermodynamics, the BPS limit, the near-horizon limit in the extremal fast and slow rotating cases, properties of black hole horizons, the existence of Killing tensors and the separability of probe scalars. [ABSTRACT FROM AUTHOR]

In the context of recently proposed holographic dualities between higher spin theories in AdS 3 and (1 + 1)-dimensional CFTs with $ \mathcal{W} $ symmetry algebras, we revisit the definition of higher spin black hole thermodynamics and the dictionary between bulk fields and dual CFT operators. We build a canonical formalism based on three ingredients: a gauge-invariant definition of conserved charges and chemical potentials in the presence of higher spin black holes, a canonical definition of entropy in the bulk, and a bulk-to-boundary dictionary aligned with the asymptotic symmetry algebra. We show that our canonical formalism shares the same formal structure as the so-called holomorphic formalism, but differs in the definition of charges and chemical potentials and in the bulk-to-boundary dictionary. Most importantly, we show that it admits a consistent CFT interpretation. We discuss the spin-2 and spin-3 cases in detail and generalize our construction to theories based on the hs[ λ] algebra, and on the sl( N,[InlineMediaObject not available: see fulltext.]) algebra for any choice of sl(2 ,[InlineMediaObject not available: see fulltext.]) embedding. [ABSTRACT FROM AUTHOR]

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. 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. Comparison with Hamiltonian and covariant phase space methods is made. All approaches are shown to agree for exact solutions and symmetries while there are differences in the asymptotic context. [ABSTRACT FROM AUTHOR]

The transition motion of a point particle around the last stable orbit of Kerr is described at leading order in the transition-timescale expansion. Taking systematically into account all self-force effects, we prove that the transition motion is still described by the Painlevé transcendent equation of the first kind. Using an asymptotically matched expansions scheme, we consistently match the quasicircular adiabatic inspiral with the transition motion. The matching requires us to take into account the secular change of angular velocity due to radiation reaction during the adiabatic inspiral, which consistently leads to a leading-order radial self-force in the slow timescale expansion. [ABSTRACT FROM AUTHOR]

New chiral boundary conditions are found for quantum gravity with matter on \(AdS_3\). The associated asymptotic symmetry group is generated by a single right-moving U(1) Kac-Moody-Virasoro algebra with \(c_R=\frac{3ℓ}{2G}\). The Kac-Moody zero mode generates global left-moving translations and equals, for a BTZ black hole, the sum of the total mass and spin. The level is positive about the global vacuum and negative in the black hole sector, corresponding to ergosphere formation. Realizations arising in Chern-Simons gravity and string theory are analyzed. The new boundary conditions are shown to naturally arise for warped \(AdS_3\) in the limit that the warp parameter is taken to zero., Physics

Classical two-dimensional Liouville gravity is often considered in conformal gauge which has a residual left and right Virasoro symmetry algebra. We consider an alternate, chiral, gauge which has a residual right Virasoro Kac-Moody algebra, and no left Virasoro algebra. The Kac-Moody zero mode is the left-moving energy. Dirac brackets of the constrained Hamiltonian theory are derived, and the residual symmetries are shown to be generated by integrals of the conserved chiral currents. The central charge and Kac-Moody level are computed. The possible existence of a corresponding quantum theory is discussed., Physics

A framework that structures the gravitational memory effects and which is consistent with gravitational electric-magnetic duality is presented. A correspondence is described between memory observables, particular subleading residual gauge transformations, associated overleading gauge transformations and their canonical surface charges. It is shown that matter-induced transitions can generate infinite towers of independent memory effects at null infinity. These memories are associated with an infinite number of conservation laws at spatial infinity which lead to degenerate towers of subleading soft graviton theorems. It is shown that the leading order mutually commuting supertranslations and (novel) superrotations are both associated with a leading displacement memory effect, which suggests the existence of new boundary conditions. [ABSTRACT FROM AUTHOR]

We propose a set of consistent boundary conditions containing the spacelike warped black holes solutions of Topologically Massive Gravity. We prove that the corresponding asymptotic charges whose algebra consists in a Virasoro algebra and a current algebra are finite, integrable and conserved. A similar analysis is performed for the timelike warped AdS3 spaces which contain a family of regular solitons. The energy of the boundary Virasoro excitations is positive while the current algebra leads to negative (for the spacelike warped case) and positive (for the timelike warped case) energy boundary excitations. We discuss the relationship with the Brown-Henneaux boundary conditions. [ABSTRACT FROM AUTHOR]

The Kerr/CFT correspondence has been recently broadened to the general extremal black holes under the assumption that the central charges from the non-gravitational fields vanish. To confirm this proposal, we derive the expression of the conserved charges in the Einstein-Maxwell-scalar theory with topological terms in four and five dimensions and check that the above assumption was correct. Combining the computed central charge with the expected form of the temperature, the Bekenstein-Hawking entropy of the general extremal black holes in four and five dimensions can be reproduced by using the Cardy formula. [ABSTRACT FROM AUTHOR]

We compute the mass, angular momenta, and charge of the Gödel-type rotating black hole solution to five-dimensional minimal supergravity. A generalized Smarr formula is derived, and the first law of thermodynamics is verified. The computation rests on a new approach to conserved charges in gauge theories that allows for their computation at finite radius.