Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2404.10083 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866917818922958848 |
|---|---|
| author | Macedo, Rodrigo Panosso Bourg, Patrick Pound, Adam Upton, Samuel D. |
| author_facet | Macedo, Rodrigo Panosso Bourg, Patrick Pound, Adam Upton, Samuel D. |
| contents | Second-order self-force calculations will be critical for modelling extreme-mass-ratio inspirals, and they are now known to have high accuracy even for binaries with mass ratios $\sim 1:10$. Many of the challenges facing these calculations are related to slow convergence of spherical-harmonic (or spheroidal harmonic) mode sums in a region containing the small companion. In this paper, we begin to develop a multi-domain framework that can evade those problems. Building on recent work by Osburn and Nishimura, in the problematic region of spacetime we use a puncture scheme and decompose the punctured field equations into a basis of Fourier and azimuthal $m$ modes, avoiding a harmonic decomposition in the $θ$ direction. Outside the problematic region, we allow for a complete spherical- or spheroidal-harmonic decomposition. As a demonstration, we implement this framework in the simple context of a scalar charge in circular orbit around a Schwarzschild black hole. Our implementation utilizes several recent advances: a spectral method in each region, hyperboloidal compactification, and an extremely high-order puncture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10083 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multi-domain spectral method for self-force calculations Macedo, Rodrigo Panosso Bourg, Patrick Pound, Adam Upton, Samuel D. General Relativity and Quantum Cosmology Second-order self-force calculations will be critical for modelling extreme-mass-ratio inspirals, and they are now known to have high accuracy even for binaries with mass ratios $\sim 1:10$. Many of the challenges facing these calculations are related to slow convergence of spherical-harmonic (or spheroidal harmonic) mode sums in a region containing the small companion. In this paper, we begin to develop a multi-domain framework that can evade those problems. Building on recent work by Osburn and Nishimura, in the problematic region of spacetime we use a puncture scheme and decompose the punctured field equations into a basis of Fourier and azimuthal $m$ modes, avoiding a harmonic decomposition in the $θ$ direction. Outside the problematic region, we allow for a complete spherical- or spheroidal-harmonic decomposition. As a demonstration, we implement this framework in the simple context of a scalar charge in circular orbit around a Schwarzschild black hole. Our implementation utilizes several recent advances: a spectral method in each region, hyperboloidal compactification, and an extremely high-order puncture. |
| title | Multi-domain spectral method for self-force calculations |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2404.10083 |