Gravitational Waveforms, Soft Theorems and Scattering Amplitudes

• Carlo Heissenberg (IPhT, CEA Saclay)

Room: Salle de conférence du Château de Meudon (bât. 9) Scattering amplitudes provide a convenient strategy to calculate gravitational-wave observables characterizing compact binaries in the weak-field or post-Minkowskian (PM) regime, when the two objects remain far away from each other. Conversely, classical soft theorems encode exact information about the dynamics of such systems and do not rely on the PM expansion, while of course restricting to the low-frequency band of the gravitational wave spectrum. In this talk I will illustrate recent progress on these two complementary approaches to the gravitational two-body problem, focusing in particular on predictions for the waveforms, the radiated energy spectrum and the angular momentum loss.

Non-conservative Hamiltonian perturbation methods for post-Newtonian binary dynamics at 2.5PN

• Christopher Aykroyd (LTE, Observatoire de Paris)

Room: Salle de conférence du Château de Meudon (bât. 9) Non-conservative processes, such as gravitational radiation in compact binaries, are inherently challenging to describe within traditional action principles. To address this limitation, a useful strategy is to embed the system into a higher dimensional manifold, which allows the variational principle to be reframed via initial (causal) conditions. This approach has been explored both in quantum settings (the Schwinger-Keldysh formalism), and in classical settings: Galley's non-conservative principle of stationary action. Building upon Galley's principle, we present a novel extension of discrete Hamiltonian mechanics to non-conservative systems. We show that this framework can systematically recast any second-order system of ordinary differential equations as a Hamiltonian system, irrespective of prior canonical structure. In particular, we exploit our formalism by generalizing the Lie perturbation approach to dissipative systems, and then applying it to solving the equations of motion for post-Newtonian radiating binaries, departing from the point-mass ADM Hamiltonian at 2.5PN. This generalized Lie method allows for a systematic computation of both secular and oscillatory contributions to inspiral dynamics, holding promise for precision waveform modelling in next-generation gravitational wave detectors.

Exact solutions in DHOST gravity: From black holes to radiative spacetime

• Jibril Ben Achour (ENS Lyon)

Room: Salle de conférence du Château de Meudon (bât. 9) Exact solutions are crucial in our understanding of the gravitational field both for black hole and gravitational waves. In this talk, I will review the efforts in constructing exact solutions in modified gravity, focusing on the case of Degenerate Higher Order Scalar Tensor (DHOST) theories. I will underline the limitations we face so far to explore and organize the solution space of these theories, in particular the sectors relevant for the description of compact objects and gravitational waves phenomenology. In the first part, I will discuss the most recent no-hair theorem for DHOST and how suitable disformal solutions by pass its assumptions. Then, I shall discuss the key theorems of general relativity, in particular the Goldberg Sachs theorem, which single out algebraically special solutions. To that end, I will review the Newman-Penrose formalism and the Petrov classification which are key to derive these theorems. I will further show how the Petrov type allows one to identify suitable solutions with hidden symmetries. Finally, if time allows it, I will discuss the case of non-linear gravitational waves and how one provide general conditions, using the Newman-Penrose formalism, to generate tensorial gravitational waves from a disformal transformation. The main goal of the presentation is to review the key ruling structures of the solution space of general relativity and see how we can import or adapt them to study the solution space of alternatives theories of gravity.

Innermost stable circular orbit of compact binaries at the fourth post-Newtonian order

• Etienne Ligout (APC)

Room: Salle de conférence du Château de Meudon (bât. 9) We compute by means of post-Newtonian (PN) methods the innermost stable circular orbit (ISCO) of compact binaries. Two methods are used, with equivalent results: one based on the equations of motion in harmonic coordinates and one on the Hamiltonian formalism in ADM coordinates. The ISCO is deduced from an invariant stability criterion, extending the 3PN criterion of Blanchet and Iyer (2003) to the 4PN order. The heart of the derivation of this 4PN criterion is the study of the perturbation of the tail integrals appearing in the dynamics, which are non-local in time. We also explicitly show that the 4PN Lagrangian and 4PN Hamiltonian intermediate results are equivalent by deriving the relation between harmonic and ADM coordinates.