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Inverse problems for differential operators with singular boundary conditions

Blue, Decay of solutions of the Maxwell equation on the Schwarzschild background , arXiv Aksteiner, L.

Hawking Radiation and Particle Pairs Near a Black Hole

Andersson, S. Ma, C. Paganini, B. Whiting, Mode stability on the real axis , arXiv Blue, Geometry of black hole spacetimes , arXiv Blue, J. Joudioux, Hidden symmetries and decay for the Vlasov equation on Kerr spacetime, arXiv Bachelot-Motet, A. Bachelot, Waves on accelerating dodecahedral universes , arXiv Bouvier, C.

Gobin, F. Nicoleau, Local inverse scattering at fixed energy in spherically symmetric asymptotically hyperbolic manifolds , arXiv Imaging 10 , no. Kamran, F. Nicoleau, Inverse scattering at fixed energy on asymptotically hyperbolic Liouville surfaces , arXiv Nicoleau, Non-uniqueness results for the anisotropic Calderon problem with data measured on disjoint sets , arXiv Nicoleau, Direct and inverse scattering at fixed energy for massless charged Dirac fields by Kerr-Newman-de Sitter black holes , arXiv Di Menza, J.

Nicolas, Superradiance on the Reissner-Nordstrom metric , arXiv Quantum Grav. Drago, C. Volume , 8, A generalization to other set-ups is also discussed.

I review some properties of W algebras which are extensions of the Virasoro algebra in 2D conformal field theory by higher spin currents. Finally, I make some comments on an interesting discrete triality symmetry of this algebra. I will briefly review the black hole deconstruction proposal, which describes black hole microstates in terms of brane configurations consisting of fluxed D6-anti-D6 pairs surrounded by ellipsoidal D2-branes. I will then report on some progress in constructing the corresponding backreacted microstate geometries in 5-dimensional supergravity, which involve exciting the universal hypermultiplet.

After discussing the general structure of hypermultiplet solutions, I will classify susy solutions with isometries, extending earlier results of Bellorin, Meessen and Ortin. Of special importance are solutions with a toric Kahler base, which include a supersymmetric version of the Godel universe as well as new solutions relevant for black hole deconstruction.

We revisit the study of the phase structure of higher spin black holes carried out in arXiv In particular we study the low as well as high temperature regimes. We show that the Hawking-Page transition takes place in the low temperature regime. The thermodynamically favoured phase changes from conical surplus to black holes and then again to conical surplus as we increase temperature.

We then show that in the high temperature regime the diagonal embedding gives the appropriate description. We also give a map between the parameters of the theory near the IR and UV fixed points. This makes the "good" solutions near one end map to the "bad" solutions near the other end and vice versa. We revisit the description of the space of asymptotically AdS3 solutions of pure gravity in three dimensions with a negative cosmological constant as a collection of coadjoint orbits of the Virasoro group.

Each orbit corresponds to a set of metrics related by diffeomorphisms which do not approach the identity fast enough at the boundary. Orbits contain more than a single element and this fact manifests the global degrees of freedom of AdS3 gravity, being each element of an orbit what we call boundary graviton. We show how this setup allows to learn features about the classical phase space that otherwise would be quite difficult.

Black Holes in Higher Dimensions

Most important are the proof of energy bounds and the characterization of boundary gravitons unrelated to BTZs and AdS3. In addition, it makes manifest the underlying mathematical structure of the space of solutions close to infinity. Notably, because of the existence of a symplectic form in each orbit, being this related with the usual Dirac bracket of the asymptotic charges, this approach is a natural starting point for the quantization of different sectors of AdS3 gravity.

We finally discuss previous attempts to quantize coadjoint orbits of the Virasoro group and how this is relevant for the formulation of AdS3 quantum gravity. Remarkably enough, the coupling of this last term coincides with the one that appears in Critical Gravity. Adopting the throat quantization pioneered by Louko and Makela, we derive the mass and area spectra for the Schwarzschild-Tangherlini black hole and its anti-de Sitter AdS generalization in arbitrary dimensions.

We obtain exact spectra in three special cases: the three-dimensional BTZ black hole, toroidal black holes in any dimension, and five-dimensional Schwarzshild-Tangherlini -AdS black holes. For the remaining cases the spectra are obtained for large mass using the WKB approximation.

In the asymptotically AdS case on the other hand, it is the mass spectrum that is equally spaced. Our exact results for the BTZ black hole with Dirichlet boundary conditions agree with those obtained previously via completely different methods.

Duke Mathematical Journal

Massive gravity in three dimensions accepts several different formulations. Recently, the 3-dimensional bigravity dRGT model in first order form, Zwei-Dreibein gravity, was considered by Bergshoeff et al. We revisit this assertion and conclude that there are sectors on the space of initial conditions, or subsets of the most general such model, where this mode is absent. But, generically, the theory does carry 3 degrees of freedom and thus the Boulware-Deser mode is still active.

Our results also sheds light on the equivalence between metric and vierbein formulations of dRGT model. The slow relaxations which may occur in many-body systems when quenched to a co-existence regime below their critical point can be characterised by the breaking of time-translation-invariance and dynamical scaling, with a non-trivial value of the dynamical exponent z. It is possible to formulate variants of conformal invariance for a given value of z, which can be different from 1.

Non-uniqueness results for the anisotropic Calderón problem with data measured on disjoint sets

The requirement of co-variance of the non-equilibrium two-time response functions under these transformations permits to predict the form of their universal scaling f unctions, in relatively good agreement with simulational data in specific models. Here, we present recent results on decomposable, but not irreducible representations of these algebras, which generalise known results from logarithmic conformal invariance.

In this talk I shall describe the addition of fermionic impurities to the unquenched ABJM Chern—Simons-matter theory using the holographic approach. Using this setup, I will analyze the straight flux tube embeddings and the corresponding fluctuation modes of the D6-branes. In any CFT with a semiclassical holographic dual, we show that the first law of entanglement entropy for ball-shaped regions in the CFT is equivalent to the linearized gravitational equation of motion in the bulk, including arbitrary higher curvature corrections.

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The bulk equations of motion imply the first law of entanglement in the dual CFT, and conversely, the first law can be used to reconstruct the linearized bulk geometry solely from knowledge of the entropy function. Additionally, the first law can be used to derive the holographic dictionary for the stress tensor. In particular, this approach provides a simple alternative to holographic renormalization for computing its expectation value in arbitrary higher derivative gravitational theories.

It also carries holographic information about the additional operators in the boundary theory which couple to the bulk metric in higher curvature gravity. We discuss general properties of Higher Spin algebras in different space-time dimensions. We discuss finite dimensional truncations of these algebras, that exist in 2, 3 and 5 dimensions. Recently Lysov and Strominger [arXiv In this paper we show that the non-relativistic fluid dual to vacuum Einstein gravity does not satisfy the Petrov type I condition at next order, unless additional constraint such as the irrotational condition is added.

We discuss the procedure both on the finite cutoff surface via the non-relativistic hydrodynamic expansion and on the highly accelerated surface via the near horizon expansion. I will discuss what we learned from the measurement of the mass of this particle. In particular, I will consider the implications for the Standard Model, for theories beyond the Standard Model such as supersymmetry and composite models , and for the stability of the scalar potential.

We use a pure spinor approach reminiscent of generalized complex geometry. Without the need for any Ansatz, the system determines uniquely the form of the metric and fluxes, up to solving a system of ODEs. The simplest model to consider is Einstein-Maxwell gravity, and the ground state of the system is described by Reissner-Nordstrom black hole where all the charge is carried by the black hole. However, it turns out that this solution is unstable to the formation of both fermionic and bosonic matter, corresponding in the dual field theory to the creation of a Fermi surface and the onset of superconductivity, respec- tively.

We consider Einstein-Maxwell system coupled to a perfect fluid of charged fermions and a charged scalar field. We compute the free energy and show that these new solutions are thermodynami- cally favoured when they exist.


Moreover, we find evidence for a continuous phase transition between the holographic superconductor and the new solutions. Using Generalised Geometry it is easy to see that the internal manifold has to have SU 2 structure. We will then focus on coset and group manifolds and we will look for examples allowing for scale separation. We will also show that, for constant warp factor, it is not possible to have sourceless solutions. This is realized by a generalization of Hitchin's equation. This framework encompasses a rich class of theories including superconformal and confining ones.

In a first part we will sketch a proof of the fact that pure analytic Hadamard states exist on any globally hyperbolic, analytic spacetime having an analytic Cauchy surface. The importance of analytic Hadamard states comes from the fact that they satisfy the Reeh-Schlieder property. In a second part we will use the Wick rotation to prove the existence and Hadamard property of the Hartle-Hawking state on a spacetime having a stationary, bifurcate Killing horizon, thereby extending a result of Sanders which dealt with the static case.

Instability of enclosed horizons. The proof relies on an iteration scheme at each step of which one solves a linear wave-type equation globally. The analysis takes place on a suitable compactification of 4 to a manifold with corners whose boundary hypersurfaces correspond to spacelike, null, and timelike infinity; I will describe how the asymptotic behavior of the metric can be deduced from the structure of simple model operators at these boundaries.

By "consistently", one means that the formal series for the interacting quantum field operators in this theory have the desired properties such as Einstein causality term-by-term , and that a renormalization prescription exists which depends "locally and covariantly" on the spacetime geometry. These works were a culmination of a long development and not only involved new tools e.

A crucial new feature appearing in this theory is gauge-invariance. In fact, it is non-trivial both to formulate this invariance at the quantum level, and to show that a renormalization prescription exists which is compatible with it and the other features mentioned before. In this talk, I sketch the essential ideas of renormalization theory in curved spacetime including some new developments relating it to Fedosov quantization by Collini and myself, and also related results due to Taslimitehrani and Zahn.

We consider the question of how to extend this relationship to curved scattering backgrounds, focusing on certain 'sandwich' plane waves. We calculate the 3-point amplitudes on these backgrounds and find that a notion of double copy remains in the presence of background curvature: graviton amplitudes on a gravitational plane wave are the double copy of gluon amplitudes on a gauge field plane wave. This is non-trivial in that it requires a non-local replacement rule for the background fields and the momenta and polarization vectors of the fields scattering on the backgrounds.

It must also account for new 'tail' terms arising from scattering off the background. These encode a memory effect in the scattering amplitudes, which naturally double copies as well. Dappiaggi and N. Pinamonti on Hadamard quasifree states and their properties constructed out the structure of null horizons or null infinity or cosmological horizons.

Dappiaggi, V. Moretti, N. The question of its genericity, especially when talking about the peeling of the Weyl tensor of an Einstein spacetime, was controversial for several decades after Penrose's paper. For Einstein's equations, the question is now essentially settled, but given an Einstein spacetime, it is not clear whether there is a large class of Cauchy data giving rise to solutions with a good peeling.

We extended recently the results to linear and non linear scalar fields on the Kerr geometry in a joint work with Pham Truong Xuan. We shall recall the history of the subject, describe the principles of the approach developed with Lionel Mason and talk about the specific features of our work for Kerr metrics. This parameter is constant in space and time and relies essentially on global structures: a stationary spacetime and a KMS state. In this talk I will review a local definition temperature for massless free scalar fields, proposed by Buchholz, Ojima and Roos.