Green functions of the Regge-Wheeler and Teukolsky equations in Schwarzschild spacetime
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| Format: | Preprint |
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2026
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| _version_ | 1866911498192814080 |
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| author | Aruquipa, David Q. Casals, Marc |
| author_facet | Aruquipa, David Q. Casals, Marc |
| contents | We present a calculation of the full retarded Green functions of the Regge-Wheeler and Teukolsky equations obeyed by gravitational field perturbations of Schwarzschild spacetime. We perform the calculations for spacetime points along: (i) a timelike circular geodesic (where null-separated points are not at caustics); and (ii) a static worldline (where null-separated points are at caustics). These Green functions show a 4-fold singularity structure away from caustics, and 2-fold at caustics (similarly to the case of scalar field perturbations, which we also reproduce). Physical oscillations near the singularities appear in the gravitational case, which were not present in the scalar case. We obtain our results by developing various numerical and analytical methods. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_07747 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Green functions of the Regge-Wheeler and Teukolsky equations in Schwarzschild spacetime Aruquipa, David Q. Casals, Marc General Relativity and Quantum Cosmology High Energy Physics - Theory We present a calculation of the full retarded Green functions of the Regge-Wheeler and Teukolsky equations obeyed by gravitational field perturbations of Schwarzschild spacetime. We perform the calculations for spacetime points along: (i) a timelike circular geodesic (where null-separated points are not at caustics); and (ii) a static worldline (where null-separated points are at caustics). These Green functions show a 4-fold singularity structure away from caustics, and 2-fold at caustics (similarly to the case of scalar field perturbations, which we also reproduce). Physical oscillations near the singularities appear in the gravitational case, which were not present in the scalar case. We obtain our results by developing various numerical and analytical methods. |
| title | Green functions of the Regge-Wheeler and Teukolsky equations in Schwarzschild spacetime |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2603.07747 |