arXiv subjects

Anna M. Wolz

Publications and source records attributed to Anna M. Wolz.

5 recordsLinked to original sources

arXiv2026

Environmental Effects in Post-Minkowskian Dynamics: Effective Field Theory, Feynman Rules, and Ward Identities for Compact Objects in Relativistic Fluids

We develop a hydrodynamic effective field theory for the gravitational dynamics of compact objects moving through an inviscid fluid environment. The fluid is described by the effective theory of perfect fluids, whose Goldstone phonons are kept as explicit fields coupled to gravity. We establish a consistent power counting for the resulting Feynman rules and derive the propagators and interaction vertices through four points in $D$ dimensions, together with the generalized on-shell Ward identities they obey. These identities relate amplitudes with an external graviton to those with the graviton replaced by a phonon, and thus provide nontrivial checks on higher-order calculations. As an application, we recover the leading-order relativistic dynamical-friction force from the tree-level amplitude for single-phonon emission. This work is a first step towards a toolkit for incorporating environmental effects into the scattering-amplitude pipeline used in post-Minkowskian calculations.

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arXiv2026

Gravitational Compton Amplitude to All Orders in Perturbation Theory

We show how amplitudes from the scattering of gravitational waves off compact objects in worldline effective field theory can be efficiently computed to arbitrary order in Newton's constant $G$. Our approach solves an effective wave equation for the partial-wave amplitude in which Wilson coefficients (tidal Love numbers) enter through boundary conditions at short distances. We then perform the sum over partial waves to obtain the momentum-space Compton amplitude in terms of elliptic polylogarithms. We reproduce recent results through $\mathcal{O}(G^4)$ and obtain new predictions up to $\mathcal{O}(G^7)$, with Love numbers first contributing at $\mathcal{O}(G^5)$. We find the first ultraviolet divergence in a classical gravitational amplitude at $\mathcal{O}(G^7)$, showing that a pure point-particle description is not consistent in general relativity. Matching to black hole perturbation theory, we show that static Love numbers vanish on-shell and predict subleading non-zero Schwarzschild black hole Love numbers.

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arXiv2025

Analyticity of the Black Hole S-Matrix

We establish the analytic structure of the S-matrix in the complex-frequency plane for classical wave scattering on a Schwarzschild background in four space-time dimensions. Our argument relies on the analytic continuation of the gravitational potential, with the singularity behind the horizon playing a crucial role. We find that in the lower half-plane the partial-wave amplitudes are analytic except for the quasinormal-mode poles and the branch cut associated with late-time tails. As a direct consequence of causality, the retarded Green's function and absorption amplitude are analytic in the upper-half plane. We show, however, that Stokes phenomena can obstruct this analyticity domain from carrying over to the elastic amplitude, which instead develops a branch-cut in the upper-half plane. We also determine the effect of infrared (IR) regulators on the analytic structure, showing that polynomial boundedness requires a sharp lower bound on the IR cutoff in terms of the Schwarzschild radius.

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arXiv2025

The hierarchical three-body problem at $\mathcal{O} (G^2)$

Employing techniques from scattering amplitudes and effective field theory, we model the dynamics of hierarchical triples, which are three-body systems composed of two bodies separated by a distance $r$ and a third body a distance $ρ$ away, with $r \ll ρ$. We apply the method of regions to systematically expand in the small ratio $r/ρ$ and illustrate this approach for evaluating Fourier transform integrals, which have been the bottleneck for deriving complete results in position space. In the limit where the distant third body is much heavier than the other two, we derive new analytic results in position space for the three-body conservative potential at $\mathcal{O}(G^2)$ and at leading and next-to-leading order in $r/ρ$. We also derive new results for arbitrary masses in the rest frame of the distant particle. Our results are exact in velocity, and can be used in analyses involving both bound and unbound hierarchical triples in astrophysical systems.

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arXiv2024

Records from the S-Matrix Marathon: Gravitational Physics from Scattering Amplitudes

These lecture notes explain how classical gravitational physics emerges from scattering amplitudes. We emphasize the role of different kinematic regimes in probing various aspects of bound and unbound problems, as illustrated by the Hydrogen atom example. Classical predictions of General Relativity, such as the Shapiro time delay and perihelion precession, emerge from these considerations. We also explain a number of recent approaches to probing black hole physics from the perspective of amplitudes, including applications of worldline effective field theory in astrophysics, predictions of gravitational waveforms, and the hierarchical three-body problem. These notes are based on a series of lectures held during the S-Matrix Marathon workshop at the Institute for Advanced Study on 11--22 March 2024.

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