Gravitational scattering amplitudes from curved space
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915877987811328 |
|---|---|
| author | Eriksen, Carl Jordan |
| author_facet | Eriksen, Carl Jordan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20261 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Gravitational scattering amplitudes from curved space Eriksen, Carl Jordan General Relativity and Quantum Cosmology High Energy Physics - Theory 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. |
| title | Gravitational scattering amplitudes from curved space |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2603.20261 |