Mathematical Physics of Gravity and Symmetry 2025

23 juin 2025, 09:00 → 26 juin 2025, 17:00 Europe/Paris

Amphithéâtre Anne L'Huillier (ENS Lyon)

Dimitrios Tsimpis, Etera Livine (ENS de Lyon), Hugo Roussille (ENS Lyon), Jibril Ben Achour (Ecole Normale Supérieure - Lyon / Arnold Sommerfeld Center - Munich), Marc Geiller, Stefan Hohenegger (IP2I Lyon), Sylvain Carrozza (Université Bourgogne Europe), Taro Kimura (Université Bourgogne Europe)

Description

This workshop aims at discussing recent advances in the theory of gravity, with a particular emphasis on its symmetry aspects and related topics, such as asymptotic symmetries, black hole perturbation theory, holography, quasi-normal modes, and quantum gravity. The objective of this workshop is to convene leading experts in these extensive fields to initiate and foster new interdisciplinary collaborations.

Previous edition: Mathematical Physics of Gravity and Symmetry, November 2024, Dijon

Speakers

Suddhasattwa Brahma	U. Edinburgh
Johann Chevrier	IMB
Adolfo Cisterna	Charles U.
Adrien Fiorucci	CPHT
Jahanur Hoque	ULB
Simon Iteanu	Orsay
Jose Luis Jaramillo	IMB
Valentine Maris	ENS de Lyon
Clara Montagnon	ENS de Lyon
Silvia Nagy	Durham
Marios Petropoulos	CPHT
Aymeric Proust	ENS de Lyon
Manuel Del Piano	Naples
Bernard Raffaelli	IMB
Antoine Rignon-Bret	U. Lorraine
Quantin Vigneron	NCU
Antoine Vincenti	ENS de Lyon
Corentin Vitel	IMB
Wolfgang Wieland	FAU Erlangen
Yuki Yokokura	RIKEN
Céline Zwikel	PI

Venue

ENS de Lyon

Amphithéâtre Anne L'Huillier

46 allée d'Italie, 69007 Lyon

https://maps.app.goo.gl/MJgZ1zA79fsHXg4X9

 

   

lun. 23 juin

1 Emergent cosmological spacetime from Matrix Models

I will review recent results, and list outstanding challenges, of deriving an emergent cosmological spacetime from string-theoretic models. I will give a proposal for how a metric can be coarse-grained from abstract matrix degrees of freedom, and how one naturally gets a scale-invariant spectrum of primordial perturbations in this model, without introducing arbitrary tunable parameters, by considering a thermal state in this model. In the second part, I will describe how a "collective-field" formalism can be employed to see the emergence of spacetime from matrix quantum mechanics.

Orateur: Suddhasattwa Brahma

intro.pdf

Lyon_workshop_2025.pdf

10:30 Coffee break

2 Aspects of spherically-symmetric spacetime towards gravity-matter interaction

Orateur: Yuki Yokokura

12:00 Lunch break

3 Lie Point Symmetries in Electrovacuum: New Type I spacetimes in Einstein Theory

Orateur: Adolfo Cisterna

Lyon Talk.pdf

15:00 Coffee break

4 Test-Field vs Physical Quasi-Normal Modes of a modified BH solution

In the context of the general effort to model black hole dynamics, and in particular their return-to-equilibrium through quasi-normal modes, it is crucial to understand how much test-field perturbations deviate from physical perturbations in modified gravity scenarios. On the one hand, physical perturbations follow the modified Einstein equations of the considered extension of general relativity. The complexity of those equations can quickly escalate with extra fields and non-linear couplings. On the other hand, test-field perturbations, with negligible back-reaction on the space-time geometry, describe the propagation of both matter fields and spin s = 2 gravitational waves on the black hole geometry. They are not subject to the intricacies of the modified Einstein equations, and only probe the background spacetime metric. If their physics were to not deviate significantly from physical perturbations, they would be especially useful to investigate predictions from quantum gravity scenarios which lack explicit detailed Einstein equations. Here we focus on a specific modified gravity solution – BCL black holes in scalar-tensor theories – for which physical perturbations and related QNM frequencies have already been studied and computed numerically. We compute the test-field QNM frequencies and compare the two QNM spectra. This provides a concrete example of the significant differences arising between test-fields and physical perturbations, and flags unphysical deviations related to the test-field framework.

Orateur: Clara Montagnon

Talk_Gravity___Sym_2025_Lyon.pdf

5 Asymptotically-flat spacetimes with twist

Orateur: Antoine Vincenti

Pres.pdf

6 Axial perturbations of black holes with primary scalar hair

Orateur: Simon Iteanu

Presentation_Iteanu.pdf

mar. 24 juin

7 Carrollian momenta from anti de Sitter

Defining an energy-momentum tensor for asymptotically flat spacetimes seems to be of interest in its own right, or for possible holographic applications. That said, the role it could play is less clear than for anti de Sitter, bearing in mind that in the flat case an infinite number of data are needed on scri to reconstruct a solution. I will show that besides the Carrollian geometric structure at null infinity, this infinite set dubbed Carrollian momenta emerge as the Laurent coefficients of the AdS energy-momentum tensor expanded in powers of the cosmological constant. The present analysis unravels the role of the boundary Cotton tensor.

Orateur: Marios Petropoulos

Marios-Lyon-2025-50.pdf

10:30 Coffee break

8 Boundedness of Gravitational Wave Luminosity from Non-Perturbative Quantum Effects of Gravity

Orateur: Wolfgang Wieland

12:00 Lunch break

9 Holographic Derivation of BMS Flux-Balance Laws

The main challenges in formulating a holographic correspondence for asymptotically flat spacetimes stem from the null nature of the conformal boundary and the non-conservation of gravitational charges in the presence of bulk radiation. In this talk, I will present the systematic and mathematically robust approach to understanding and deriving the associated flux-balance laws from geometric principles defined intrinsically at the boundary. I will begin by reviewing key aspects of the geometry at null infinity, known as conformal Carroll geometry. I will highlight that the boundary affine connections contain degrees of freedom that naturally act as sources encoding radiation in a holographic framework. I will then derive flux-balance laws for an effective field theory formulated at the boundary, using novel techniques that introduce “hypermomenta” as the responses to fluctuations in the boundary connection. These equations reproduce the celebrated BMS flux-balance laws in a convenient boundary gauge. Based on arxiv:2505.00077 in collaboration with S. Pekar, P. Marios Petropoulos and M. Vilatte.

Orateur: Adrien Fiorucci

FluxBalance_Lyon_2025.pdf

15:00 Coffee break

10 An effective metric description of quantum black holes

Black holes provide a unique setting to explore quantum gravity, where semiclassical effects and quantum corrections can modify their observable properties. In this talk, I will present an effective metric approach to describe such effects in a model-independent way. The deformations of the metric are captured by a priori unknown functions of a physical observable of the spacetime, expressed as self-consistent Taylor series expansions. I will discuss how this framework remains independent of the specific choice of the observable and how it impacts black hole shadows and thermodynamic properties. Finally, I will compare the results with predictions from specific quantum gravity models, highlighting the potential for connecting theoretical approaches with observational signatures.

References: https://arxiv.org/abs/2307.13489 , https://arxiv.org/abs/2403.12679 , https://arxiv.org/abs/2412.13673 , https://arxiv.org/abs/2504.20810 .

Orateur: Manuel Del Piano

11 Local Unitary Invariant Polynomials in the Limit of Large Dimension -- Characterization and Distinction of Quantum States

In this presentation, we explore the structure of multipartite quantum entanglement through the lens of local unitary (LU) invariants. We begin with the bipartite case, where entanglement entropy admits a clear LU-invariant characterization via the Schmidt decomposition. We then extend the discussion to multipartite systems, where no canonical notion of spectrum exists and the classification problem becomes significantly more challenging. Motivated by the search for universal features of entanglement that typically emerge in the large-dimension limit, we focus on geometrically inspired quantities—most notably, the notion of compatibility. Building on these ideas, we introduce a tree-based construction of LU-invariant polynomials, offering both an algebraic and combinatorial framework to probe the structure of entanglement. We further analyze the ability of these invariants to distinguish between inequivalent quantum states. Finally, we discuss potential connections with holography, where such invariants may, in the context of random tensor networks, admit dual interpretations as geometric cuts in the bulk.

Orateur: Johann Chevrier

MathPhy_Lyon_Johann.pdf

12 Scale separation on AdS$_3\times S^3$ with and without supersymmetry

String theory predicts extra spatial dimensions. The compactification of these extra dimensions give mass to particles. Knowing the spectrum of the particles is thus a central task to answer the question of which particle is observable. Moreover, to make sense of a lower-dimension theory one assumes that the extra dimensions are '' small ''. However, usually this is not the case, especially if one considers an AdS external space. This problem is know as '' scale separation '' and is another challenge to phenomenological string theory. This talk will be about computing the spectrum of a 6 dimensional theory around an ${\rm AdS}_3$ background and showing that these vacua are scale-separated.

Orateur: Aymeric Proust

proust_presentation_24_06_2025_16h30.pdf

mer. 25 juin

13 Simplicity and Universality in Binary Black Hole mergers: from Caustics-Diffraction to Integrability

The waveform of a binary black hole (BBH) coalescence appears to be both simple and universal. A natural question to ask is the following: is the BBH waveform “boring” or, rather, “elegant”? This talk is structured in two parts, a first one with a decidedly heuristic (and admittedly boldly ambitious) flavor and a second part in which ideas of the first part are cast in a more modest (but still ambitious) setting. Specifically, the first part presents a hierarchical research program aiming at probing such simplicity and universality of BBH dynamics. Adopting a (bottom-up) “asymptotic-reasoning” approach, we define different layers for the treatment of the problem, starting by modeling the BBH merger waveform in terms of the Airy function realised as the universal diffraction pattern on a fold-caustic and, passing through the Painlevé-II transcendent as a non-linear generalisation of Airy, proposing a “wave-mean flow” description of the dynamics with an effective separation of “fast and slow” degrees of freedom, the latter described by an integrable system. This scheme implements a view of the BBH waveform as ‘elegant’, potentially providing a probe into the fundamental structure of a (self-dual) sector of the gravitational theory. The second part of the talk starts exploring these ideas by casting such “fast/slow” gravitational dynamics in the setting of a hyperboloidal approach to (linear) scattering on black holes: ‘slow’ degrees of freedom are frozen and encoded into the background geometry, whereas the scattered field provides the ‘fast’ degrees of freedom. The associated non-selfadjoint infinitesimal generator of the dynamics presents a neat separation into bulk and boundary parts, providing an avenue for the exploration of the symmetries underlying, respectively, slow and fast degrees of freedom, plausibly realised as a semidirect action of bulk symmetries onto the (asymptotic/)boundary symmetries. The talk provides both an invitation to C. Vitel’s talk and an update to recent work by J. Besson on non-modal aspects of the non-selfdjoint (fast) dynamics of the scattered field.

Orateur: Jose Luis Jaramillo

fAiry_BBHmerger_2025_Lyon.pdf

10:30 Coffee break

14 Lessons from the self-dual sector

I will show how the self-dual sector can be a useful tool to study asymptotic symmetries, and associated infinite algebras, both in flat space and in backgrounds relevant to cosmology.

Orateur: Silvia Nagy

12:00 Lunch break

15 Black hole free energy

Orateur: Antoine Rignon-Bret

15:00 Coffee break

16 Integrability Aspects of Perturbed Black Holes: a Lax Pair Hyperboloidal Approach

Black hole (BH) perturbation theory allows to decouple Einstein perturbative equations into wave-like master equations. In the spirit of a ”wave-mean flow” description of the dynamics, the background potential and master functions would be respectively cast as ”slow” and ”fast” degrees of freedom (DoF): the ”slow” DoF would underlie a nonlinear integrable dynamics (in the sense of isospectral deformations) on which the ”fast” DoF evolve according to a linear dynamics. We address such gravitational scattering problem by using a hyperboloidal scheme for the spacetime. In such a framework, the infinitesimal time generator of the dynamics turns into a non-selfadjoint operator and the related master equations become neatly separated between bulk and asymptotic contributions. Our focus is on identifying a Lax-pair formulation with the associated Hamiltonian structure(s) that underpin the integrability features, starting from a (weak) adjoint spectral problem that is formulated in terms of an energy dependent Schrödinger operator.

Orateur: Corentin Vitel

VITEL_ENS_Lyon_Juin_2025.pdf

17 Noncommutative geometry and deformed Minkowski space-time

Noncommutative geometry provides a representation of space-time in terms of associative algebras of operators. The final goal is to end up with a "quantum space-time" which should encode quantum gravity effects at an effective level. Recently, the construction of such quantum space-times has been investigated and led to deformations of the usual Minkowski space-time.

Orateur: Valentine Maris

workshopGRlyon.pdf

jeu. 26 juin

18 Debate on quadrupole formula in de Sitter

It is well-known that gravitational fields from an isolated system depend on the time varying quadrupole moment of the source. Quadrupole formula provides an estimate of the energy loss due to gravitational radiation. The first proposed quadrupole formula for gravitational waves in de Sitter was derived by Ashtekar, Bonga, Kesavan (ABK). We point out that a consistent quadrupolar truncation is needed to upgrade the ABK formula. We also compare our result to a recently obtained result of Bonga, Bunster, Perez. We write the quadrupole formula in two distinct ways which allow standard flat limit and negative definite energy flux in de Sitter. The existence of several proposals for the quadrupole formula suggests that fundamental requirements on the uniqueness of the quadrupole formula, such as the enforcement of gauge invariance, are still missing.

Orateur: Jahanur Hoque

10:30 Coffee break

19 Topology dependent background connection in gravitation: Motivations and consequences for cosmology

General relativity (GR) is equipped with one connection: the Levi-Civita connection of the Lorentzian metric. I will present a (parameter-free) modification of GR where a second affine connection dependent on the topology of the Universe is introduced. The presentation will be an overview of the motivations and consequences for cosmology of this framework. In particular, I will discuss the Galilean and Carrollian limits, definitions of mass, curved inflationary models, Bianchi models and observational tests.

Orateur: Quentin Vigneron

2025_06_Lyon.pdf

12:00 Lunch break

20 Celestial Symmetries of Black Hole Horizons

I will present a novel correspondence between the gravitational phase space at null infinity and the subleading phase space for finite-distance null hypersurfaces, such as black hole horizons. Using Newman-Penrose formalism and an off-shell Weyl transformation, this construction transfers key structures from asymptotic boundaries to null surfaces in the bulk—for instance, a notion of radiation. Imposing self-duality conditions, I will identify the celestial symmetries and construct their canonical generators for finite-distance null hypersurfaces. This framework provides new observables for black hole physics.

Orateur: Céline Zwikel

Talk_Celestial_Symm.pdf

15:00 Coffee break

21 A Weyl law for black hole quasinormal modes

In this talk, I will present a recent conjecture about a Weyl's law for black hole quasinormal mode frequencies, that recovers the structural features of the standard Weyl's law for the eigenvalues of Laplacian-like operators in compact regions. More precisely, we propose that the asymptotic behavior of the counting function of quasinormal frequencies follows a power-law depending on the dimension of space and on two structural properties of the underlying black hole geometry, namely the redshift effect, through the surface gravity, and the trapped set of null geodesics. This conjecture will be explicitly motivated on the example of the Schwarzschild black hole, and then generalized to a generic stationary black hole geometry, extending (and being inspired by) the Weyl's law proven by Dyatlov and Zworski some years ago.
Based on: Phys.Rev.D110,104008 (2024), in collaboration with J.L. Jaramillo, R.P. Macedo, O. Meneses-Rojas, L. Al Sheikh.

Orateur: Bernard RAFFAELLI

BR_Présentation_WorkshopENSLyon2025.pdf