arXiv subjects

Adrien Druart

Publications and source records attributed to Adrien Druart.

7 recordsLinked to original sources

arXiv2026

Symplectic mechanics of relativistic spinning compact bodies. III. quadratic-in-spin integrability in Type-D Einstein spacetimes: persistence and breakdown

We investigate the integrability of spinning compact body dynamics at quadratic order in spin in four-dimensional Einstein spacetimes admitting a non-degenerate Killing--Yano tensor. Working within the Mathisson--Papapetrou--Tulczyjew--Dixon framework under the Tulczyjew--Dixon spin supplementary condition, we model the spin-induced quadrupole with a deformability parameter $\kappa$, where $\kappa=1$ corresponds to black holes. The dynamics is formulated as a Hamiltonian system on a 10-dimensional physical phase space obtained by Dirac--Bergmann reduction. For $\kappa=1$, we establish Liouville--Arnold integrability at quadratic order in spin by constructing five independent, Poisson-commuting first integrals, including a generalization of the Carter constant and the R\"udiger constant to quadratic-in-spin order in Einstein spacetimes beyond Kerr. For $\kappa \neq 1$, the R\"udiger and Carter constants are no longer conserved; integrability does not persist at this order. All our results are carried out in a covariant manner and numerically verified, and Kerr is recovered as a special case. These results show that integrability can extend beyond Kerr and beyond the linear-in-spin regime, while its breakdown for $\kappa \neq 1$ points to the spin-induced quadrupole as a decisive probe of compact body structure.

gr-qc↗

arXiv2023

Waveform Modelling for the Laser Interferometer Space Antenna

LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the beginnings of inspirals that will venture into the ground-based detectors' view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA's discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This white paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome.

gr-qc↗

arXiv2023

Generalized Carter constant for quadrupolar test bodies in Kerr spacetime

We establish the existence of a deformation of the usual Carter constant which is conserved along the motion in a fixed Kerr background of a spinning test body possessing the spin-induced quadrupole coupling of a black hole. The conservation holds perturbatively up to second order in the test body's spin. This constant of motion is obtained through the explicit resolution of the conservation constraint equations, employing covariant algebraic and differential relations amongst covariant building blocks of the Kerr background. For generic spin-induced quadrupole couplings, which describe compact objects such as neutron stars, we obtain a no-go result on the existence of such a conserved quantity.

gr-qc↗

arXiv2023

The Motion of Test Bodies around Kerr Black Holes

This thesis aims to explore the properties of the motion of finite size, compact test bodies around a Kerr black hole in the small mass-ratio approximation. The small body is modelled as a perturbation of Kerr geometry, neglecting its gravitational back-reaction but including deviations from a purely geodesic motion by allowing it to possess a non-trivial internal structure. Such a body can be accurately described by a worldline endowed with a collection of multipole moments. Hereafter, we shall always consider the multipole expansion truncated at quadrupole order. Moreover, only spin-induced quadrupole moment will be taken into account, thus discarding the presence of any tidal-type deformation. For astrophysically realistic objects, this approximation is consistent with expanding the equations of motion up to second order in the body's spin magnitude. The text is structured as follows. The first part is devoted to an extended review of geodesic motion in Kerr spacetime, including Hamiltonian formulation and classification of timelike geodesics, with a particular emphasis put on near-horizon geodesics of high spin black holes. The second part introduces the equations of motion for extended test bodies in generic curved spacetime, also known as Mathisson-Papapetrou-Dixon (MPD) equations. The third part discusses conserved quantities for the MPD equations in Kerr spacetime, restricting to the aforementioned quadrupole approximation. Finally, the covariant Hamiltonian formulation of test body motion in curved spacetime is presented, and an Hamiltonian reproducing the spin-induced quadrupole MPD equations is derived. It is shown that the constants of motion obtained in the previous part directly arise while solving the Hamilton-Jacobi equation at first order in the spin magnitude. Some expectations regarding the computation at quadratic order close the discussion.

gr-qc↗

arXiv2021

Complete set of quasi-conserved quantities for spinning particles around Kerr

We revisit the conserved quantities of the Mathisson-Papapetrou-Tulczyjew equations describing the motion of spinning particles on a fixed background. Assuming Ricci-flatness and the existence of a Killing-Yano tensor, we demonstrate that besides the two non-trivial quasi-conserved quantities, i.e. conserved at linear order in the spin, found by Rüdiger, non-trivial quasi-conserved quantities are in one-to-one correspondence with non-trivial mixed-symmetry Killing tensors. We prove that no such stationary and axisymmetric mixed-symmetry Killing tensor exists on the Kerr geometry. We discuss the implications for the motion of spinning particles on Kerr spacetime where the quasi-constants of motion are shown not to be in complete involution.

gr-qc↗

arXiv2021

Analytical edge power loss at the lower hybrid resonance: comparison with ANTITER IV and application to ICRH systems

In non-inverted heating scenarios, a lower hybrid (LH) resonance can appear in the plasma edge of tokamaks. This resonance can lead to large edge power deposition when heating in the ion cyclotron resonance frequency (ICRF) range. In this paper, the edge power loss associated with this LH resonance is analytically computed for a cold plasma description using an asymptotic approach and analytical continuation. This power loss can be directly linked to the local radial electric field and is then compared to the corresponding power loss computed with the semi-analytical code ANTITER IV. This method offers the possibility to check the precision of the numerical integration made in ANTITER IV and gives insights in the physics underlying the edge power absorption. Finally, solutions to minimize this edge power absorption are investigated and applied to the case of ITER's ion cyclotron resonance heating (ICRH) launcher. This study is also of direct relevance to DEMO.

physics.plasm-ph↗

arXiv2020

Near-horizon geodesics of high-spin black holes

We provide an exhaustive and illustrated classification of timelike and null geodesics in the near-horizon region of near-extremal Kerr black holes. The classification of polar motion extends to Kerr black holes of arbitrary spin. The classification of radial motion leads to a simple parametrization of the separatrix between bound and unbound motion. Furthermore, we prove that each timelike or null geodesic is related via conformal transformations and discrete symmetries to spherical orbits and we provide the explicit mappings. We detail the high-spin behavior of both the innermost stable and the innermost bound spherical orbits.

gr-qc↗