More Nonlinearities? II. A Short Guide of First- and Second-Order Electromagnetic Perturbations in the Schwarzschild Background
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915624480931840 |
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| author | Aly, Fawzi Mansour, Mahmoud A. Stojkovic, Dejan |
| author_facet | Aly, Fawzi Mansour, Mahmoud A. Stojkovic, Dejan |
| contents | We study second-order electromagnetic perturbations in the Schwarzschild background and derive the effective source terms for Regge-Wheeler equation which are quadratic in first-order gravitational and electromagnetic perturbations. In addition to the induced mixed quadratic modes, we find that linear gravitational modes are also excited, with amplitudes dependent on the electromagnetic potential. A toy model involving a Dirac delta function potential demonstrates mixing of linear gravitational and electromagnetic perturbations with frequencies \( ω^{(1)} \) and \( Ω^{(1)} \), resulting in the second-order QNM mixing in the electromagnetic field at \( Ω^{(2)} =Ω^{(1)} + ω^{(1)} \). This complements prior work in \cite{aly2024nonlinearities} on the second-order gravitational perturbation mixing and highlights potential applications in multi-messenger astrophysics for systems observed by LIGO-Virgo-KAGRA (LVK) and upcoming LISA. We also study first-order perturbations due to a point charge and show it could be reduced to a one-dimensional path integral. Within the toy model, we investigate the first-order electromagnetic perturbation due to a radially free-falling single charge \( q \) and radial dipole moment \( p = q η\), employing semi-analytical and numerical methods. For the dipole case, we show that the QNM perturbation is excited with a nearly constant amplitude. Future work will focus on incorporating mixing in more realistic potentials and exploring numerical approach in the context of rotating spacetimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01441 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | More Nonlinearities? II. A Short Guide of First- and Second-Order Electromagnetic Perturbations in the Schwarzschild Background Aly, Fawzi Mansour, Mahmoud A. Stojkovic, Dejan General Relativity and Quantum Cosmology High Energy Physics - Phenomenology High Energy Physics - Theory Mathematical Physics 83C35 (primary), 83C57, 83-XX, 83C05, 85A40 (secondary) We study second-order electromagnetic perturbations in the Schwarzschild background and derive the effective source terms for Regge-Wheeler equation which are quadratic in first-order gravitational and electromagnetic perturbations. In addition to the induced mixed quadratic modes, we find that linear gravitational modes are also excited, with amplitudes dependent on the electromagnetic potential. A toy model involving a Dirac delta function potential demonstrates mixing of linear gravitational and electromagnetic perturbations with frequencies \( ω^{(1)} \) and \( Ω^{(1)} \), resulting in the second-order QNM mixing in the electromagnetic field at \( Ω^{(2)} =Ω^{(1)} + ω^{(1)} \). This complements prior work in \cite{aly2024nonlinearities} on the second-order gravitational perturbation mixing and highlights potential applications in multi-messenger astrophysics for systems observed by LIGO-Virgo-KAGRA (LVK) and upcoming LISA. We also study first-order perturbations due to a point charge and show it could be reduced to a one-dimensional path integral. Within the toy model, we investigate the first-order electromagnetic perturbation due to a radially free-falling single charge \( q \) and radial dipole moment \( p = q η\), employing semi-analytical and numerical methods. For the dipole case, we show that the QNM perturbation is excited with a nearly constant amplitude. Future work will focus on incorporating mixing in more realistic potentials and exploring numerical approach in the context of rotating spacetimes. |
| title | More Nonlinearities? II. A Short Guide of First- and Second-Order Electromagnetic Perturbations in the Schwarzschild Background |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Phenomenology High Energy Physics - Theory Mathematical Physics 83C35 (primary), 83C57, 83-XX, 83C05, 85A40 (secondary) |
| url | https://arxiv.org/abs/2411.01441 |