Jibril Ben Achour
Titre: Acceleration of charged particles in the Kerr magnetosphere: An electrogeodesic approach
Abstract: The launch of relativistic jets of plasma on astrophysical to cosmological scales is observed in a variety of astrophysical sources, from active galactic nuclei to X-ray binaries. While these jets can be reproduced by general relativistic magneto-hydrodynamics (GRMHD) and particle-in- cells (GRPIC) simulations of the dynamical Kerr magnetosphere, the development of analytic models to describe the physics of the jets has remained limited. A key challenge is to analytically describe the individual trajectories of accelerated charged particles, which ultimately build up the jet and emit radiation. In this talk, I will review a first simple but fully analytical model of jet launching from the Kerr magnetosphere based on the motion of charged particles. To that end, I will review the condition for the integrability of electrogeodesic motion in the Kerr monopole magnetosphere allowing one to study the ejection of charged particles near the poles. Based on this, I will discuss (i) a criterion for the rotation axis to constitute a stable latitudinal equilibrium position, thereby representing an idealized jet, (ii) the expression for the magnetic frame-dragging effect, and (iii) the condition for an asymptotic observer to measure blueshifted particles emanating from the black hole surroundings. This will show that particles can be accelerated only in a specific region whose maximal radius depends on the spin and magnetization of the black hole. Alongside these results, I will review the role of the explicit and hidden symmetries when building models for the Kerr magnetosphere.
Based on: https://arxiv.org/abs/2601.05048
Eugeny Babichev
Title: Beyond circularity
Abstract: The Kerr metric enjoys a special symmetry known as circularity, which is normally assumed when constructing rotating black hole solutions in alternative theories of gravity and when building Kerr-mimicker models. In this talk I will examine how justified this assumption is and what happens when it breaks. Working within a geometrically natural gauge, the circularity conditions are solved analytically and translated into algebraic relations among metric components, enabling controlled study of circularity-breaking deformations. Explicit analytical examples of non-circular Kerr deformations are presented, highlighting how the horizon can lose its Killing nature even when its location and the ergosphere remain unchanged. These results lay the groundwork for more general parametrizations of rotating black holes and their observational signatures beyond general relativity.
Laura Donnay
Title: Null infinity and the black hole horizon: new conserved quantities from a geometric duality
Abstract: I will present a unified treatment for the boundary geometry of asymptotically flat spacetimes and black hole horizons. This geometric duality implies an exact inversion isometry for extremal, non-rotating horizons, which will be used to relate and derive new infinite towers of conserved quantities.
Sebastian Gurriaran
Title: Non-linear instability of the Kerr Cauchy horizon near timelike infinity
Abstract: The Kerr metrics model rotating vacuum black holes, and are expected to play a central role in the long-time description of generic solutions to the Einstein vacuum equation. They present the disturbing feature that determinism breaks down inside the black hole, beyond the Cauchy horizon. Penrose's Strong Cosmic Censorship conjecture states that this behavior is however unstable and vanishes upon small perturbations. I will present a recent work which proves that, assuming a non-linear Price's law-type estimate near the event horizon, in generic perturbations of Kerr black holes ruled by the full, non-linear, Einstein vacuum equation, a singularity forms at the Cauchy horizon near timelike infinity. This singularity - at the Lipschitz level for the metric - prevents the unphysical extensions and recovers determinism.
Marc Herzlich
Title: From the ADM mass to a topological invariant of low-dimensional
manifolds
Abstract: Initially defined in the context of General Relativity, the ADM mass is an important invariant of Riemannian asymptotically flat manifolds. Some 25 years ago, L. Habermann used it to answer a question in pure Riemannian geometry : finding a canonical metric in each conformal class of Riemannian metrics with positive scalar curvature on a compact manifold of dimension 3, 4, or 5. Despite the importance of the question in geometry, the Habermann metric seems to have escaped further notice. In a joint work with Emmanuel Humbert (Tours), we study its volume, which may lead to an interesting new topological invariant of low-dimensional manifolds.
Tamanna Jain
Title: Post-Minkowskian, Effective-one-body formalism, and Numerical Relativity : beyond GR+Standard Model Theories
Abstract: In this talk, I will present our recent work on post-Minkowskian EFT for scalar-tensor theories and boson stars. We first derive the analytical expressions of the scattering angle using PM-EFT techniques for both the cases, and in particular provide the first analytical treatment of boson stars as a two-body problem. We then derive the effective-one-body description of these systems. We then compare analytic results to the scattering angle extracted from sequences of numerical-relativity simulations at fixed energy, varying impact parameter, and coupling strength. We find excellent agreement for both the cases. In particular for boson stars, the very good agreement exhibits the attractive (repulsive) effect of in-phase (out-of-phase) binaries. For small impact parameters, where the stars approach more closely before separating to infinity, the scalar-field interaction is found to dominate.
Alexandros Kehagias
Juan Valiente Kroon
Title: Conformal geodesics and timelike infinity —revisiting the semiglobal stability of the Minkowski spacetime
Abstract: The seminal result by H. Friedrich on the semiglobal stability of the Minkowski spacetime shows that hyperboloidal initial data for the Einstein field equations which is suitably close to data for the Minkowski spacetime and conformally smooth gives rise to a future development which is future geodesically complete and has the same global structure as the comparable region in the Minkowski spacetime. Moreover, the resulting spacetime is conformally smooth and the generators of null infinity intersect at a point describing timelike infinity. In this talk I will show how a gauge based on the properties of a particular type of conformal invariants, the so-called conformal geodesics, gives rise to an alternative conformal representation of this class of spacetimes in which timelike infinity is described by a hyperboloid describing the endpoints of timelike geodesics. This representation provides an implementation of “scri-fixing” —that is, a gauge in which the location of null infinity is described as the locus of points with a fixed spatial coordinate. Finally, it will be shown how this conformal representation is naturally adapted to the use of ideas and methods of Melrose’s school of microlocal analysis. This observation opens the possibility of obtaining generalisations of Friedrich’s semiglobal results for spacetimes with polyhomogeneous asymptotics.
Ludovic Souetre
Title: The homogeneous Robin boundary conditions for asymptotically Anti-de Sitter spaces
Abstract: Modelled on the Anti-de Sitter space, asymptotically Anti-de Sitter spaces can be defined as Lorentzian manifolds that possess a timelike conformal boundary. Due to their lack of global hyperbolicity, finding asymptotically Anti-de Sitter solutions to the Einstein equations (necessarily with a negative cosmological constant) through the Cauchy problem requires tackling the latter as an initial boundary value problem. In this talk, I will present the two known types of geometric boundary conditions leading to the local existence and uniqueness of solutions in dimension 4: the Dirichlet boundary conditions, which were introduced by Friedrich in 1995, and the homogeneous Robin boundary conditions, which I introduced.
Pierre Vanhove
Title: Exact Metric solutions from a cubic action
Abstract: In this talk we describe a method for deriving exact metric solutions from a cubic worldline action in every dimensions from an amplitude computation. With this formalism one can derive the geodesic motions of a test particle in such background. The same formalism is suitable for the self-force expansion in a post Minkowskian formalism.
This is based on work with Stavros Mougiakakos and work in progress.