Amplitudes and EFT approach

• Chia-Hsien Shen

Intro to black hole perturbation theory and self-force

• Leor Barack

NR, EOB and Data Analysis

• Patricia Schmidt

Free discussion

NR, EOB and Data Analysis

• Geraint Pratten

Amplitudes and EFT approach

• Chia-Hsien Shen

BHPT Tutorial

• Barry Wardell

Intro to black hole perturbation theory and self-force

• Leor Barack

NR, EOB and Data Analysis

• Patricia Schmidt

Intro to self-force EFT

• Nabha Shah

Intro to black hole perturbation theory and self-force

• Leor Barack

Intro to Self-force EFT

• Nabha Shah

BHPT Tutorial

• Barry Wardell

Hands-on session: NR, EOB and Data Analysis

• Patricia Schmidt

High-Precision Dynamics and Waveforms in Two-Body Scattering

• Thibault Damour

Amplitudes for Gravitational Waves

• David Kosower

I review relativistic perturbative computations relevant to gravitational-waves physics.

WEFT at fifth post N/M order

• Rafael Porto

I review recent developments in the WEFT approach to compact binary dynamics, both in the PN and PM domains, to fifth order in the perturbative expansion.

Numerical Simulations of Binary Black Hole Encounters

• Harald Pfeiffer

Binary black hole encounters are the general-relativisic generalization of the Newtonian two-body problem, and represent the majorit of observed gravitational waves (GW). Precise knowledge about the interaction between two black holes and the emitted GWs are of high importance for finding and analysing GW signals, as well as to deepen the understanding of the structure and solutions of Einstein's equations. Such knowledge is obtained by numerical calculations and perturbation methods like post-Newtonian and post-Minkowskian expansions, as well as the gravitational self-force formalism, and the last years have seen rich new results in the overlap between different methods. This talk summarizes recent advances in numerical relativity for binary black holes on eccentric and hyperbolic orbits, and for high mass-ratio. It then elucidates how numerical relativity and perturbation methods combine in the quest to understand properties of general relativity and to support gravitational wave science.

Discussion session

• Jan Plefka

Gravitational radiation from hyperbolic orbits: comparison between SF, PM, PN and NR

• Niels Warburton

In this talk will present the latest gravitational self-force (GSF) calculations for the radiation from hyperbolic orbits. In the first part of the talk I will focus on the radiated energy and comparisons with post-Minkowskian (PM), post-Newtonian and numerical relativity results as described in arXiv:2512.02274. In the secondary part I will present preliminary results for the radiated angular momentum and the gravitational wave memory.

Hybrid Self-Force and Post-Newtonian Waveform models - an opportunity for Post-Minkowskian Theory?

• Josh Mathews

In this talk, I’ll give an overview of self-force-based hybrid gravitational wave models that incorporate results from post-Newtonian theory. I’ll highlight that the hybridisation procedure is carefully designed with intuition from common resummations in post-Newtonian and post-Minkowskian theory. I’ll conclude with a sketch of the opportunity for these hybrid models to incorporate scattering results from post-Minkowskian theory.

Post-Minkowskian theory, Numerical Relativity and Effective-One-Body models

• Piero Rettegno (Polytechnic University of Turin)

The analysis of gravitational-wave events requires fast and accurate theoretical predictions. I focus on Effective-One-Body (EOB) models informed by Post-Minkowskian (PM) results and Numerical Relativity (NR) simulations. I compare analytical and numerical results for binary scatterings, including spin and tidal effects. Finally, I discuss the use of PM results for bound systems by means of a Lagrangian formalism.

Perturbative QFT for Gravitational Waves: Nonlocal-in-time dynamics @ 5PM

• Gregor Kälin

In recent years, techniques from perturbative quantum field theory have driven significant progress in the Post-Minkowskian (PM) expansion of binary black hole dynamics. A key challenge in this framework arises from conservative, nonlocal-in-time contributions, which obstruct a straightforward analytic continuation from scattering states to bound orbits via the boundary-to-bound (B2B) dictionary. In this talk, I will present a practical resolution based on a hybrid subtract-and-add scheme that consistently combines PM, Post-Newtonian (PN), and self-force (SF) results. This approach enables the controlled treatment of nonlocal effects and yields new state-of-the-art results for the conservative dynamics at 5PM order, including contributions up to 10th order in the self-force expansion.

Discussion session

• Jan Steinhoff

Poster session

When eccentricities "tick up''

• Maarten van de Meent

The dissipation of energy and angular momentum through the emission of gravitational waves dampens the eccentricity of compact binaries. This is a well-known fact in gravitational wave theory. However, there is a notable well-documented exception to this rule: in extreme mass-ratio inspirals the eccentricity will initially decrease during the inspiral, but will ``tick-up'' just before the binary transitions to its final plunge. We here give a simple explanation for this behaviour, showing that this the expected universal behaviour for eccentric systems transitioning through a last stable orbit.

Modelling black hole scattering using comoving hyperboloidal coordinates

• Aditya Vaswani

In recent years, the gravitational wave community has seen growing interest in modelling scattering events between 2 black holes (BH) since such events serve to better probe regions of strong gravity close to the primary BH. While some progress on this has been made using the post-Minkowskian approximation using techniques from effective field theory and scattering amplitudes, a complimentary approach is to use the Gravitational Self Force (GSF) which is more suited to analysing motion in the strong field. In this talk, I describe how these events can be modelled for self-force applications using a numerical scheme based on hyperboloidal slices that are comoving with the smaller particle. Furthermore, I will show how this scheme circumvents the divergences that plagued earlier time-domain implementations.

Black hole scattering in the strong-field regime: Merging post-Minkowskian theory with numerical methods

• Oliver Long

Recent advances in modelling unbound binary black hole interactions have been driven by the application of scattering amplitude methods to generate results within the post-Minkowskian (PM) expansion. However, this expansion breaks down when approaching the strong-field regime, where large curvature effects become non-negligible. In this talk, I will show how data from numerical relativity simulations and self-force (SF) calculations can be used as benchmarks to validate state-of-the-art PM expressions. Additionally, I will show how strong-field SF information can be used to resum the PM series, providing accurate predictions for scattering angles and radiative quantities across all separations.

Waveform modeling within the effective one body approach: new perspectives

• Alessandro Nagar

I will briefly summarize the status of effective-one-body (EOB) based waveforms for generic binaries (spin precession, eccentricity, scattering) and then suggest new avenues for theoretical development coming from both the post-Minkowskian approach and from (revisited) black hole perturbation theory.

Discussion session (Chris Kavanagh)

Dissipative observables for black hole scattering

• Rodolfo Russo

I will use Black Hole Perturbation Theory (BHPT) to study dissipative observables such as the radiative and absorbed fluxes of energy and angular momentum. I will focus on the case of black hole scattering in the Post-Minkowskian regime and discuss to what extent it is possible to reconstruct the full observables from the BHPT expansion.

Surfing the shockwave with black hole response theory

• Lara Bohnenblust

In this talk, we develop a black-hole response formulation of worldline quantum field theory (WQFT) tailored to the gravitational self-force (SF) expansion. By integrating out the primary black hole’s worldline and graviton fluctuations, we obtain an effective action built from black-hole response functions. In this, the one-point response function encodes the exact background metric, the two-point response function describes the scattering of a gravitational wave off the black hole, and higher-point functions provide effective vertices for a systematic gravitational SF expansion. As a first application, we consider a massless primary source, corresponding to the Aichelburg-Sexl shockwave or an ultra-boosted black hole. We show that the one-point response resums to the exact shockwave metric. Next, we discuss the computation of the exact in G two-point response by resumming the full post-Minkowskian series. We conclude with an outlook on how to obtain the 1SF impulse and waveform in the high-energy regime with this framework.

Non linear memory from reverse unitarity

• Alessandro Georgoudis

I will present a recent computation of the nonlinear gravitational-wave memory in two-body scattering, using scattering amplitudes and soft theorems in the weak-field post-Minkowskian regime. The effect first appears at NNLO PM, and I will show how its evaluation reduces to simpler, lower-point cut two-loop integrals.

Gravitational Sommerfeld Effects

• Chih-Hao Chang

In the effective field theory (EFT) description of compact binary inspirals, the radiated gravitational waveform receives universal corrections from gravitational background, the so-called "tail" effects, that resum into the "Sommerfeld factor". We derive a closed-form expression for the Sommerfeld factor and present a systematic framework to compute it at high orders by combining EFT with black hole perturbation theory, including induced tidal responses. We prove that the phase of the Sommerfeld factor is exactly half of the elastic Compton scattering phase shift when tidal interactions are conservative. We further establish a new renormalization group equation for the radiative multipole moments. These high-order perturbative results provide new avenues for improving waveform resummation.

Discussion session (Chia-Hsien Shen)

Self-Force From Response Theory

• Jitze Hoogeveen

We develop an efficient framework for the computation of gravitational Self-Force (SF) dynamics with Worldline Quantum Field Theory (WQFT). This “response theory” constructs an effective action for the self-forced secondary, expanded in terms of response functions. These response functions encode all SF dynamics and are interpreted as classical off-shell n-point graviton correlation functions. We discuss in length how SF dynamics may be obtained from response functions, when supplemented by 0SF dynamics. The framework is then explicitly applied to gravitational scattering in the Aichelburg-Sexl background describing a massless black hole. The prerequisite 0SF dynamics is explicitly computed, and promising work towards 1SF discussed.

Kerr Black Hole Scattering: An On-Shell Approach to Conserved Quantities and Integrability

• Dogan Akpinar

Amplitudes and worldline methods have emerged as powerful tools for studying the gravitational two-body problem. In particular, they have enabled major progress in the computation of scattering observables for spinning black holes at high post-Minkowskian orders. In this talk, we will build on these developments to investigate the integrability properties of Kerr black hole scattering, both in the probe limit and beyond. We will begin by reviewing the radial action and the recently introduced Dirac bracket formalism, which together motivate a notion of asymptotic integrability. Using these tools, we will show that this integrability persists to higher orders in spin than previously established. Finally, we will discuss spin-shift symmetry, a striking and still not fully understood property of spinning amplitudes, and show how, when combined with integrability constraints, it leads to a powerful bootstrap of the radial action.

Analytical Fluxes from Generic Schwarzschild Geodesics

• Majed Khalaf

In this talk, I present an analytic method for computing gravitational-wave fluxes from bound Schwarzschild geodesics with arbitrary eccentricity. Our approach systematically expands the Fourier coefficients of the emitted radiation in a Chebyshev basis, allowing them to be reduced to sums of Keplerian-like Fourier coefficients previously derived in the Quantum Spectral Method. Because the construction does not rely on a small-eccentricity expansion, it applies to a broad range of bound eccentric orbits. As an illustration, we implement the method using a 15PN-expanded input and find that it reproduces the total flux for the validation case (p,e)=(12.5,0.5) to relative accuracy 10^{-5}, while for the stronger-field orbit (p,e)=(10,0.8) it yields weighted mode-by-mode errors below 10^{-6} for the selected dominant modes analyzed. These results provide an analytic route to frequency-domain flux calculations relevant to EMRI modelling.

Metric of a Star: A Recursive multipolar Post-Minkowskian Construction

• Tabasum Rahnuma

We construct the exterior metric of a stationary compact source within the multipolar post-Minkowskian (MPM) formalism and develop a recursive momentum-space reformulation of the construction. The MPM framework solves the Einstein equations outside a compact source perturbatively in Newton's constant, decomposing the metric into symmetric trace-free mass and current multipole moments. In this momentum space, the multipolar structure emerges naturally from the recursive field equations, simplifying tensor structures and clarifying how multipole moments enter at successive PM orders. Crucially, the nonlinearities of the Einstein equations reduce in this picture to the iterative evaluation of bubble integrals, making explicit the nonlinear multipolar interactions, including monopole–quadrupole, quadrupole-quadrupole, and higher-order couplings. As a consistency check, we match the generic multipolar solution to the Kerr metric generated independently by a similar recursive formulation, verifying that the construction reproduces the correct Kerr multipole structure, which includes its infinite tower of moments, and thus captures the nonlinear structure of rotating vacuum solutions.

Discussion session (Kanghoon Lee)