Tag Archive

Current Events in 2025

• Lichnerowicz Conference, 11 to 13 June 2025, Institut HENRI POINCARE, 11 rue Pierre et Marie Curie, 75005 Paris
• Seminar on Mathematical General Relativity, 2024–2025, Laboratoire Jacques-Louis Lions, Sorbonne Université, 4 Place Jussieu, 75252 Paris
• ANR Project “Einstein constraints: past, present, and future” (Einstein PPF), by Erwann Delay (Avignon), Philippe G. LeFloch (Sorbonne),  Romain Gicquaud (Tours)

Highlights from Key Past Events in 2015

• Three-Month Program on MATHEMATICAL GENERAL RELATIVITY — Institut Henri Poincaré, Paris
• GENERAL RELATIVITY: A CELEBRATION OF THE 100th ANNIVERSARY – Paris, November 16 to 20, 2015

Journées Relativistes — Relativistic Days

Location: INSTITUT HENRI POINCARE

11 rue Pierre et Marie Curie, 75005 Paris

Paris, 11 to 13 June 2025

SPEAKERS
Xavier Bekaert (IDP, Tours) PDF file here
Laura Bernard (Observatoire de Paris) PDF file here
Jean-Pierre Bourguignon (IHES) PDF file here
Erwann Delay (Avignon) PDF file here
Gustavo Dotti (Cordoba, Argentina) PDF file here
Alberto Farina (Picardie) PDF file here
Paul Gauduchon (Palaiseau) PDF file here
Yuxin Ge (Toulouse) PDF file here
Romain Gicquaud (IDP, Tours) PDF file here
Yannick Herfray (IDP, Tours) PDF file here
Emmanuel Humbert (IDP, Tours) (blackboard talk)
Yvette Kosmann-Schwarzbach (Paris) PDF file here + text here
David Langlois (Paris Cité) PDF file here
Bruno Le Floch (LPTHE, Sorbonne) PDF file here
Marc Mars (Salamanca) PDF file here
Filipe Mena (Lisbon) PDF file here
Jérémie Szeftel (LJLL, Sorbonne) PDF file here
Alex Vaño-Viñuales (Palma de Mallorca) PDF file here
Michael Volkov (IDP, Tours) PDF file here

SCHEDULE: download the SCHEDULE HERE

Starting at 8:55am on Wednesday, and closing at 5:15pm on Friday

ORGANIZERS

Luc Blanchet (Institut d’Astrophysique de Paris)
Eric Gourgoulhon (LUX, Observatoire de Paris & CNRS)
José-Luis Jaramillo (IMB, Université Bourgogne Europe)
Bruno Le Floch (LPTHE, Sorbonne Université & CNRS)
Philippe G. LeFloch (LJLL, Sorbonne Université & CNRS)

++++++ POSTER OF THE CONFERENCE +++++++

FUNDING

Agence Nationale de la Recherche Project 23-CE40-0010-02 : Einstein constraints: past, present, and future. Investigators: Erwann Delay (Avignon), Romain Gicquaud (IDP, Tours), and Philippe G. LeFloch

European Network MSCA Staff Exchange Project 101131233 : Einstein gravity and nonlinear waves

LUX, Observatoire de Paris and IMB, Université de Bourgogne Europe

… Departure from IHP at the end of the conference…

TITLE and ABSTRACT

Xavier BEKAERT

BMS particles at null infinity

Abstract. Generic unitary irreducible representations (UIRs) of the Bondi-Metzner-Sachs (BMS) group are considered. They are shown to describe quantum superpositions of (Poincaré) particles propagating on inequivalent gravity vacua. This follows from reconsidering McCarthy’s classification of BMS group UIRs through a unique, Lorentz-invariant but non-linear, decomposition of supermomenta into hard and soft pieces.

Laura BERNARD

Gravitational wave tests of generic EFT-inspired theories of gravity

Abstract. Current agnostic tests of gravity with gravitational waves are plagued by a lack of realistic deviations, making it difficult to interpret such detections with respect to specific theories. In this talk, I present a dictionary that identifies the scaling of deviations with the objects’ masses and the leading order post-Newtonian corrections in generic theories constructed through an Effective Field Theory approach based on curvature. In particular, I will demonstrate that a vast set of theories only deviates from General Relativity beginning at a relatively high order. I will also clarify some subtleties of the application of the PN-EFT formalism to higher-curvature EFT theories.

Jean-Pierre BOURGUIGNON (Nicolaas Kuiper Honorary Professor at IHÉS)

André Lichnerowicz, a pioneer in the development of Differential Geometry at the frontier with Theoretical Physics

Abstract. In the middle of the 20th century, some major actors have succeeded in putting Differential Geometry much more centre stage than it used to be: Élie Cartan, Chern Shiing-Shen, Isadore M. Singer, Sir Michael Atiyah, Eugenio Calabi and of course André Lichnerowicz. This process had a lot to do with the development of new concepts and the appropriation for the field of new tools coming in particular from Analysis and Topology. In almost all cases Lichnérowicz played a key role through research articles and well appreciated books. The purpose of this lecture is two-fold: first, to describe this transformation with an emphasis on some issues to which Lichnerowics gave a lot of attention; second, to highlight some of the interactions I had with him with very clear, friendly and rewarding messages.

Erwann DELAY

Two remarkable differential operators acting on symmetric two-tensors

Abstract. On a Riemannian manifold of dimension three or higher, we introduce two differential operators acting on (fields of) trace-free symmetric 2-tensors. The first, a second-order operator, is a conformally covariant operator, similar to the Yamabe Laplacian on functions. It can be used to test the stability of certain Einstein metrics. The second, a fourth-order operator, acts as a machine for TT-tensors (symmetric 2-tensors that are both trace-free and divergence-free) on Einstein manifolds, as it allows any trace-free symmetric 2-tensor to be transformed into a TT-tensor, with many such tensors being obtained in this way. This operator can also be used to approximate a less regular TT-tensor by a smooth TT-tensor. On a Ricci-flat manifold, the restriction of these two operators to TT-tensors corresponds to the Lichnerowicz Laplacian and its square.

Gustavo DOTTI

Obstructions for trapped submanifolds

Abstract. We introduce the concept of k−future convex spacelike/null hypersurface Σ in an n + 1 dimensional spacetime and prove that no k−dimensional trapped submanifold can be tangent to Σ from its future side. As a consequence, k-dimensional closed trapped submanifolds cannot be found in open spacetime regions foliated by such hypersurfaces. In gravitational collapse scenarios, specific hypersurfaces of this kind act as past barriers for trapped submanifolds. Examples will be given of (3+1) spacetime regions containing trapped loops (k = 1) but no closed trapped surfaces (k = 2) and of how trapped loops could be used as an early indicator of black hole formation in numerical relativity.

Alberto FARINA

Classification results, rigidity theorems and semi-linear PDEs on Riemannian manifolds: a P-function approach

Abstract. We consider solutions to critical and sub-critical semilinear elliptic PDEs on complete, noncompact Riemannian manifolds and study their classification as well as the effect of their presence on the underlying manifold. When the Ricci curvature is non-negative, we prove both the classification of positive solutions to the critical equation and the rigidity for the ambient manifold. The same results are established for solutions to the Liouville equation on Riemannian surfaces. Our results are obtained via an appropriate P-function whose constancy implies the classification of both the solutions and the underlying manifold.

Paul GAUDUCHON

On a class of gravitational instantons

Abstract. A Kähler metric is called extremal if its scalar curvature is a Killing potential, i.e. is the moment relative to the Kähler form of a Hamiltonian Killing vector field; it is called toric extremal if the latter belongs to a maximal, effective Hamiltonian toric action preserving the whole Kähler structure. The presence of such a Kähler structure in the conformal class of a class of four-dimensional gravitational instantons of ALF type, including the Euclidean version of well-known Lorentzian spaces, as well as the one-parameter family of instantons discovered in 2011 by Yu Che and Edward Teo, plays a prominent role in its eventual complete classification, including a new description of the Chen–Teo instantons. This is a joint work with Olivier Biquard.

Yuxin GE

Asymptotically hyperbolic Einstein manifolds in dimension four

Abstract. Given a closed Riemannian manifold of dimension three, when will we fill in an asymptotically hyperbolic Einstein manifold of dimension 4 such that its conformal infinity is the above Riemannian metric? This problem is motivated by the correspondance AdS/CFT in quantum gravity proposed by Maldacena in 1998 et comes also from the study of the structure of asymptotically hyperbolic Einstein manifolds. In this talk, I will discuss the compactness issue of asymptotically hyperbolic Einstein manifolds in dimension four, that is, how the compactness on conformal infinity leads to the compactness of the compactification of such manifolds under the suitable conditions on the topology and on some conformal invariants. As an application, I will discuss some recent progress on the existence result.

Romain GICQUAUD

The conformal method is not conformal

Abstract. The conformal method and its variants have long been among the most effective tools for constructing solutions to the Einstein constraint equations. In this talk, I will briefly review the method and its key achievements in generating large classes of initial data. I will then present recent results showing that the conformal method is not conformally covariant. This is an undesirable feature, which I will illustrate through explicit analytic constructions and numerical evidence.

Yannick HERFRAY

Gravitational S-matrix, infrared divergences and BMS representations

Abstract. In recent years, it has been demonstrated that asymptotic symmetries of gravity (the so called BMS group) constrain the gravitational S-matrix. In particular, infrared divergences of the gravitational S-matrix are now understood to arise from to the impossibility of the usual Fock space of massless particles to ensure the conservation of the BMS charges. I will review these results taking the original perspective of representation theory. It is indeed natural to conjecture that asymptotic states suited for an infrared finite S-matrix should be unitary representations of the BMS group and thus BMS particles, rather than the usual Poincaré particles of Wigner. In a recent work with X. Bekaert and L. Donnay we constructed explicitly such BMS particles; this talk aims to serve as an introduction to X. Bekaert’s talk.

Emmanuel HUMBERT

Conformal eigenvalues of GJMS operators

Abstract. I will present recent results obtained in collaboration with R. Petrides and B. Premoselli. Our study focuses on the minimum (maximum) of the positive (negative) eigenvalues of the GJMS operator, considering metrics of volume one within a conformal class on a compact manifold. Specifically, we investigate the existence (or non-existence) of extremizers and explore their properties. This work generalizes previous results, extending the analysis of the second eigenvalue and the Yamabe operator to arbitrary orders and to GJMS operators.

Yvette KOSMANN-SCHWARZBACH

A portrait of Lichnerowicz (text here)

Abstract. I shall outline a portrait of André Lichnerowicz (1915-1998). Professor at the Collège de France, he was a great mathematician who published in mathematical physics, as well as in differential geometry, from his thesis in 1939 until his death. He was a reformer of the teaching of mathematics in France as well as a philosopher. I shall underline his collaboration with Moshé Flato when they introduced the theory of deformation quantization. He supervised numerous students, many of whom went on to become well-known mathematicians. Ten years after his death, the Lichnerowicz prize was instituted to honor young researchers in Poisson geometry, a field he pioneered in his groundbreaking article of 1977.

David LANGLOIS

Modified gravity and black holes

Abstract. This talk will present a very broad family of scalar-tensor theories of gravity that contains a single scalar degree of freedom, in addition to the usual tensor modes. These theories, known as Degenerate Higher-Order Scalar-Tensor (DHOST) theories, include and extend traditional scalar-tensor theories as well as the so-called Horndeski theories. I will then discuss black hole solutions in these theories and their perturbations, illustrated by some particular cases.

Bruno LE FLOCH

Optimal localization for the Einstein constraints

Abstract. In 2014, Carlotto and Schoen constructed initial data sets that solve the vacuum Einstein constraints and that interpolate between any asymptotically-flat vacuum solution in a cone and Euclidean space outside a wider cone.  Starting from a naive interpolation (g,K) of the two solutions to be glued, they corrected it to an exact solution that is asymptotic flat with a power-law decay slightly worse than that of (g,K).  With Philippe G. LeFloch, we reached an optimal version of their gravitational shielding by proving estimates whose power-law decay is controlled by the accuracy with which (g,K) solves the constraints, even beyond harmonic decay (namely the decay rate of black hole metrics).  At the harmonic decay rate, we encounter corrections in the kernel of asymptotic operators built from the linearized constraints.  Our work allows for very slow decay of the metrics, in which case one must define the relative ADM energy and momentum of a pair of sufficiently close initial data sets.

Marc MARS

Characterizations results of Kerr-de Sitter in any dimension

Abstract. The Kerr-de Sitter metric in arbitrary dimension was proposed by Gibbons et al. as a generalization the four dimensional Kerr-de Sitter metric obtained by Carter. While the role of particular cases of Kerr-de Sitter (such as Kerr-Myers-Perry, Schwarzschild-Tangherlini, de Sitter or Minkowski) certainly play a pivotal role in gravity, the role of Kerr-de Sitter is far less clear. In this talk I will explore local geometric properties that characterize the Kerr-de Sitter metric in arbitrary dimension. The main tool will be to analyze its asymptotic data at null infinity. In particular, I will show that the simplest (non-trivial) asymptotic data gives rise to a class of spacetimes called Kerr-de Sitter-like and I will identify what makes Kerr-de Sitter special within this class. Based on this, I will present various characterization properties of the Kerr-de Sitter-like metrics in arbitrary dimension.

Filipe MENA

Initial value problem in modified theories of gravity

Abstract. The question we address in this talk is how can one formulate a (locally) well-posed initial value problem in modified theories of gravity. We review recent results including scalar-tensor and Einstein-Cartan theories before focusing on a spherically evolution problem in f(R) theory.

Jérémie SZEFTEL

The nonlinear stability of Kerr for small angular momentum

Abstract. I will introduce the celebrated black hole stability conjecture according to which the Kerr family of metrics are stable as solutions to the Einstein vacuum equations of general relativity. I will then discuss the history of this problem, including a recent work on the resolution of the black hole stability conjecture for small angular momentum.

Alex VAÑO-VIÑUALES

Numerical hyperboloidal compactification: waves on FLRW and Einstein equations

Abstract. Both parts of this talk involve numerical simulations on compactified hyperboloidal slices reaching future null infinity. The first part, presenting joint work with Flavio Rossetti, focuses on the asymptotic decay of the linear wave equation on flat and hyperbolic FLRW spacetimes with a time-dependent scale factor. I will describe the setup, which allows us to recover decay rates obtained from evolutions on usual truncated Cauchy slices, and also consider solutions of a non-linear wave with self-interactions. The second part will summarize my approach using conformal compactification to free hyperboloidal evolutions of the Einstein equations. I will describe the main ingredients, present relevant results, and update on the current status towards 3D evolutions.

Mikhail VOLKOV

Black holes with electroweak hair

Abstract. We construct static and axially symmetric magnetically charged hairy black holes in the gravity-coupled Weinberg-Salam theory. Large black holes merge with the Reissner-Nordstr\”om (RN) family, while the small ones are extremal and support a hair in the form of a ring-shaped electroweak condensate carrying superconducting W-currents and up to 22% of the total magnetic charge. The extremal solutions are asymptotically RN, with a mass below the total charge, due to the negative Zeeman energy of the condensate interacting with the black hole magnetic field. Therefore, they cannot decay into RN black holes. As their charge increases, they show a phase transition, when the horizon symmetry changes from spherical to oblate. At this point, they have the mass typical for planetary size black holes of which about 11% are stored in the hair. Being obtained within a well-tested theory, our solutions are expected to be physically relevant.