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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2501.12377 |
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| _version_ | 1866929683418841088 |
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| author | Poisson, Eric |
| author_facet | Poisson, Eric |
| contents | Mukkamala and Pereñiguez recently discovered a new master function for even-parity metric perturbations of the Schwarzschild spacetime. Remarkably, this function satisfies the Regge-Wheeler equation (instead of the Zerilli equation), which was previously understood to govern the odd-parity sector of the perturbation only. In this paper I follow up on their work. First, I identify a source term for their Regge-Wheeler equation, constructed from the perturbing energy-momentum tensor. Second, I relate the new master function to the radiation fields at future null infinity and the event horizon. Third, I reconstruct the metric perturbation from the new master function, in the Regge-Wheeler gauge. The main conclusion of this work is that the greater simplicity of the Regge-Wheeler equation (relative to the Zerilli equation) is offset by a greater complexity of obtaining the radiation fields and reconstructing the metric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12377 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mukkamala-Pereñiguez master function for even-parity perturbations of the Schwarzschild spacetime Poisson, Eric General Relativity and Quantum Cosmology Mukkamala and Pereñiguez recently discovered a new master function for even-parity metric perturbations of the Schwarzschild spacetime. Remarkably, this function satisfies the Regge-Wheeler equation (instead of the Zerilli equation), which was previously understood to govern the odd-parity sector of the perturbation only. In this paper I follow up on their work. First, I identify a source term for their Regge-Wheeler equation, constructed from the perturbing energy-momentum tensor. Second, I relate the new master function to the radiation fields at future null infinity and the event horizon. Third, I reconstruct the metric perturbation from the new master function, in the Regge-Wheeler gauge. The main conclusion of this work is that the greater simplicity of the Regge-Wheeler equation (relative to the Zerilli equation) is offset by a greater complexity of obtaining the radiation fields and reconstructing the metric. |
| title | Mukkamala-Pereñiguez master function for even-parity perturbations of the Schwarzschild spacetime |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2501.12377 |