arXiv subjects

Francisco M. Blanco

Publications and source records attributed to Francisco M. Blanco.

7 recordsLinked to original sources

arXiv2026

The Magnusian generator for dissipative systems and application to leading 2.5PN radiation-reaction dynamics

The Magnusian is a phase-space function that generates finite-time evolution through nested Poisson brackets. It is related to several familiar generators of classical dynamics, including the radial action, the eikonal phase and related quantities. In this work, we extend the Magnusian framework to systems with dissipation and nonlocal-in-time interactions using the in-in formalism, also known as the Schwinger-Keldysh or Galley formalism. This framework is particularly natural for binary dynamics, where integrating out the mediating gravitational field can produce both dissipative radiation-reaction effects and hereditary, nonlocal-in-time interactions. We derive the generalized Magnusian and show that it continues to generate finite-time evolution. As an application, we construct the Magnusian for Newtonian bound motion subject to the leading 2.5PN radiation-reaction force. The resulting generator defines a discrete evolution map from one cycle to the next and describes the evolution of the system in agreement with numerical solutions.

gr-qc↗

arXiv2026

Conservative and dissipative sectors in a nonlinear scalar model for the gravitational self-force problem

When considering how self-interaction affects an object's motion, it can be convenient to decompose the self-force into conservative and dissipative pieces. As a toy model for understanding such decompositions of the gravitational self-force, we consider objects that do not affect the spacetime, but are instead coupled to a nonlinear scalar field. There is then a standard splitting of the first-order scalar self-force into conservative and dissipative components. Multiple criteria can be used to obtain this splitting, all of which imply the same result. However, the implications of these criteria generically differ at higher orders. Demanding that any reasonable conservative sector be Hamiltonian, we identify multiple possible definitions of the conservative second-order self-force. Motivations for these possibilities and their properties are discussed and relevant Hamiltonians are obtained. We assume the existence of a three-point function with certain properties that is a generalization of the Detweiler-Whiting two-point function. These results apply to the two-body problem but are restricted to unbound scattering trajectories, due to infrared divergences that arise for bound orbits.

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arXiv2026

Beyond the Separatrix: Analytic Continuation of Darwin Variables for Plunging Geodesics in Schwarzschild Spacetime

We study geodesic motion of a test particle in Schwarzschild spacetime. Bound and scattering geodesics are commonly described using Darwin variables, which provide a convenient parametrization of the radial motion. However, this description breaks down at the separatrix and does not extend straightforwardly to plunging trajectories. We construct an analytic continuation of Darwin variables that yields a real parametrization of bound, scattering, and plunging Schwarzschild geodesics, thereby providing a unified kinematical description of all types of test-mass motion. As a proof of concept, we then apply these variables to a simple non-geodesic evolution in which the energy and angular momentum are driven by a constant external force. This toy model is not intended to represent a physical radiation-reaction model, but rather to illustrate how the extended variables can be used to follow an orbit through a transition to plunge using a single orbital phase variable across the separatrix.

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arXiv2025

Nonlinearly self-interacting extended bodies move as test bodies in effective external fields

In electromagnetism, linearized general relativity, and other contexts, previous work has shown that the laws of motion which govern compact, self-interacting bodies can be obtained by applying "Detweiler-Whiting prescriptions" to the laws of motion which govern test bodies. These prescriptions replace any field which appears in a test-body law of motion with a certain effective field which is a quasilocal functional of the physical variables -- a functional that can be interpreted as a regularization procedure in a point-particle limit. We generalize these results, presenting a formalism which allows Detweiler-Whiting prescriptions to be be directly derived for extended bodies, even in nonlinear field theories. If a generating functional with particular properties can be constructed, we find effective linear and angular momenta which evolve via Mathisson-Papapetrou-Dixon equations involving appropriate effective fields. These equations implicitly incorporate all self-force, self-torque, and extended-body effects. Although our main focus is on bodies coupled to nonlinear scalar fields, we also remark on the gravitational case.

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arXiv2024

Local Hamiltonian dynamics from non-local action principles and applications to binary systems in general relativity

We consider a class of finite-dimensional dynamical systems whose equations of motion are derived from a non-local-in-time action principle. The action functional has a zeroth order piece derived from a local Hamiltonian and a perturbation in the form of a non-local functional of the trajectory on phase space. We prove that the dynamics of these systems admits a local Hamiltonian description to all order in the perturbation and we provide explicit formulae for the $\mathcal{N}^{\text{th}}$ order Hamiltonian and symplectic form in terms of the $(\mathcal{N}-1)^{\text{th}}$ order Hamiltonian flow. In the context of general relativity, these systems arise in the study of binary systems such as pairs of black holes or neutron stars in the small mass-ratio and post-Newtonian approximations. We provide applications of the formalism to binary systems in these regimes.

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arXiv2023

Motion of a spinning particle under the conservative piece of the self-force is Hamiltonian to first order in mass and spin

We consider the motion of a point particle with spin in a stationary spacetime. We define, following Witzany (2019) and later Ramond (2022), a twelve dimensional Hamiltonian dynamical system whose orbits coincide with the solutions of the Mathisson-Papapetrou-Dixon equations of motion with the Tulczyjew-Dixon spin supplementary condition, to linear order in spin. We then perturb this system by adding the conservative pieces of the leading order gravitational self-force and self-torque sourced by the particle's mass and spin. We show that this perturbed system is Hamiltonian and derive expressions for the Hamiltonian function and symplectic form. This result extends our previous result for spinless point particles.

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arXiv2022

Particle motion under the conservative piece of the self-force is Hamiltonian

We consider the motion of a point particle in a stationary spacetime under the influence of a scalar, electromagnetic or gravitational self-force. We show that the conservative piece of the first-order self-force gives rise to Hamiltonian dynamics, and we derive an explicit expression for the Hamiltonian on phase space. Specialized to the Kerr spacetime, our result generalizes the Hamiltonian function previously obtained by Fujita et. al., which is valid only for non-resonant orbits. We discuss implications for the first law of binary black hole mechanics.

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