Andres Luna

A bstract: In a previous Letter, we showed that physical scattering observables for compact spinning objects in general relativity can depend on additional degrees of freedom beyond those described by the spin vector, which can be packaged into an unconstrained spin tensor. In this paper, we provide further details on the physics of these additional degrees of freedom, whose commutation relations and Poisson brackets are inherited from the underlying Lorentz symmetry, and on their consequence on observables. In particular, we give the waveform at leading order in Newton’s constant and up to second order in the components of the spin tensor, and the conservative impulse, boost and spin kick, exhibiting spin magnitude change, through next-to-leading-order in Newton’s constant and third order in the components of the spin tensor. We provide explicit examples — a Newtonian two-particle bound system and a certain black-hole solution in an exotic matter-coupled gravitational theory — that exhibit these degrees of freedom and are described by our four-dimensional and worldline field theories. We also discuss connections between these degrees of freedom and dynamical worldline multipole moments. We construct effective two-body Hamiltonians, we demonstrate explicitly that the extra degrees of freedom beyond the spin vector are necessary to describe the complete dynamics, and we explicitly remove certain unphysical singularities. Moreover, we show that the previously proposed eikonal (or radial action) formula correctly captures observables derived from the classical Hamiltonian. Finally, we comment on possible descriptions of the additional degrees of freedom from the perspective of Goldstone’s theorem.

A bstract: We set up a procedure to systematically obtain Compton-like amplitudes in an arbitrary-spin theory, exploiting their factorization properties, and colour-kinematics duality. We furthermore investigate the constraining of Wilson coefficients for arbitrary spinning bodies and its relation to colour-kinematic duality.

We show that physical scattering observables for compact spinning objects in general relativity can depend on additional degrees of freedom in the spin tensor beyond those described by the spin vector alone. The impulse, spin kick, and leading-order waveforms exhibit such a nontrivial dependence. A signal of this additional structure is the change in the magnitude of the spin vector under conservative Hamiltonian evolution, similar to our previous studies in electrodynamics. These additional degrees of freedom describe dynamical mass multipoles of compact objects and decouple for black holes. We also show that the conservative impulse, spin kick, and change of the additional degrees of freedom are encoded in the eikonal phase.

We study the classical dynamics of spinning particles using scattering amplitudes and eikonal exponentiation. We show that observables are determined by a simple algorithm. A wealth of complexity arises in perturbation theory as positions, momenta and spins must be iteratively corrected at each order. Even though we restrict ourselves to one-loop computations at quadratic order in spin, nevertheless we encounter and resolve a number of subtle effects. Finally, we clarify the links between our work and various other eikonal approaches to spinning observables.

The double copy relates momentum-space scattering amplitudes in gauge and gravity theories. It has also been extended to classical solutions, where in some cases an exact double copy can be formulated directly in terms of products of fields in position space. This is seemingly at odds with the momentum-space origins of the double copy, and the question of why exact double copies are possible in position space — and when this form will break — has remained largely unanswered. In this paper, we provide an answer to this question, using a recently developed twistorial formulation of the double copy. We show that for certain vacuum type-D solutions, the momentum-space, twistor-space and position-space double copies amount to the same thing, and are directly related by integral transforms. Locality in position space is ultimately a consequence of the very special form of momentum-space three-point amplitudes, and we thus confirm suspicions that local position-space double copies are possible only for highly algebraically-special spacetimes.

The classical double copy relates solutions of biadjoint, gauge, and gravity theories. The ultimate origin and scope of this correspondence remains mysterious, such that it is important to build a clear physical intuition of how the double copy operates. To this end, we consider the multipole expansion of exact classical solutions. Using a recently developed twistor translation of the classical double copy, we use well-established techniques to show that the multipole moments of arbitrary vacuum type-D gravity fields are exactly related to their counterparts in gauge and biadjoint scalar theories by the single and zeroth copies. We cross-check our results using previously obtained results for the Kerr metric and also provide new results for the “square root” of the Kerr-Taub-NUT solution.

Quantum Electrodynamics (QED) serves as a useful toy model for classical observables in gravitational two-body systems with reduced complexity due to the linearity of QED. We investigate scattering observables in scalar QED at the sixth order in the charges (two-loop order) in a classical regime analogous to the post-Minkowskian expansion in General Relativity. We employ modern scattering amplitude tools and extract classical observables by both eikonal methods and the formalism of Kosower, Maybee, and O’Connell (KMOC). In addition, we provide a simplified approach to extracting the radial action beyond the conservative sector.