arXiv subjects

Carl Jordan Eriksen

Publications and source records attributed to Carl Jordan Eriksen.

4 recordsLinked to original sources

arXiv2026

Black Hole Response Theory and its Exact Shockwave Limit

We present a black hole response formalism formulated within the worldline approach to the classical gravitational two-body problem. The central objects are response functions: a hierarchy of correlators that encode, successively, the black hole's own gravitational field, the scattering of a gravitational wave off of the black-hole including recoil, and the nonlinear response to multiple gravitational perturbations. These functions serve as the natural building blocks for a systematic diagrammatic expansion in the mass ratio of a binary, the gravitational self-force expansion (SF), employing the worldline quantum field theory (WQFT) formalism. As a first application we treat an ultra-relativistic black hole, whose field is the Aichelburg-Sexl shockwave. We show that our framework reproduces the exact shockwave geometry and the trajectories of probes crossing it. Our main result is the scattering of a gravitational wave off the shockwave, computed exactly in Newton's constant by resumming the full post-Minkowskian (PM) perturbative series, which we compute for off-shell gravitons enabling later use in the SF expansion. The exact on-shell answer takes a strikingly compact form: the leading-order result is dressed by an overall phase that captures the expected infrared (Weinberg) behaviour together with a Coulomb-like scattering phase. Our results provide the basic WQFT ingredients for future 1SF computations of observables such as the impulse and waveform in the ultra high-energy regime.

hep-th↗

arXiv2026

The gravitational Compton amplitude at third post-Minkowskian order

We employ a single worldline effective field theory in a Schwarzschild--Tangherlini background to compute the gravitational Compton amplitude up to third post-Minkowskian order. By exposing the structure of infrared and forward divergences of the post-Minkowskian expansion, we are able to regulate these divergences, thereby establishing an exact and useful computational bridge to results in black hole perturbation theory. We also outline possible applications for Compton amplitudes with finite-size effects, such as spin and tidal features.

hep-th↗

arXiv2026

Gravitational scattering amplitudes from curved space

Motivated by the study of extreme mass-ratio binary systems, recent work has explored the use of curved backgrounds in computations of classical gravitational amplitudes [arXiv:2308.15304, arXiv:2308.14832, arXiv:2406.14770]. While these investigations concern the self-force expansion in the ratio of masses of the binaries, the use of curved backgrounds is interesting in its own right. In this thesis, I examine how gravitational computations can be done in a curved background. After having reviewed aspects of general relativity and the $d$-dimensional metric generated by a point mass (known as the Schwarzschild-Tangherlini solution), I quantize general relativity on an arbitrary background and compute Feynman rules for gravity in two cases: when the background is flat, and when it is a Schwarzschild-Tangherlini background. I then outline worldline quantum field theory. Using this newly-developed perturbation theory for the partition function of a worldline coupled to gravity in a curved background, I reformulate the perturbative expansion of the Compton amplitude, which describes the scattering of a graviton off a compact object. Having established this framework, I compute the first and second post-Minkowskian contributions to the Compton amplitude. Both are shown to match the results obtained from a flat-space computation. In addition, the second-order amplitude displays the expected infrared behavior and agrees with earlier results on massless gravitational scattering.

gr-qc↗

arXiv2025

The gravitational Compton amplitude from flat and curved spacetimes at second post-Minkowskian order

We utilize various computational techniques in flat and curved backgrounds to calculate the classical gravitational Compton amplitude up to the second post-Minkowskian order. Our novel result supports the use of worldline quantum field theory in non-trivial background spacetimes to obtain new theoretical insights that can both enhance computational efficiency and provide useful cross-checks of results, particularly in the context of classical binary black hole mergers.

hep-th↗