Uniform Energy Bound for Maxwell-Higgs Equations on Reissner-Nordström Spacetimes
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913535472173056 |
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| author | Mulyanto Atmaja, Ardian N. Akbar, Fiki T. Gunara, Bobby E. |
| author_facet | Mulyanto Atmaja, Ardian N. Akbar, Fiki T. Gunara, Bobby E. |
| contents | In this paper, we prove the uniform energy bound for the Maxwell-Higgs system in the exterior region of Reissner-Nordström black holes. By employing an integrated local energy decay (ILED) estimate in combination with the Sobolev embedding theorem on a compact Riemannian manifold, we derived $L^\infty$ bounds for the fields. These results were then used to obtain a bound for the conformal energy of the system using the Cauchy-Schwarz inequality and Hardy-type inequalities. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_04724 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniform Energy Bound for Maxwell-Higgs Equations on Reissner-Nordström Spacetimes Mulyanto Atmaja, Ardian N. Akbar, Fiki T. Gunara, Bobby E. Analysis of PDEs General Relativity and Quantum Cosmology Mathematical Physics In this paper, we prove the uniform energy bound for the Maxwell-Higgs system in the exterior region of Reissner-Nordström black holes. By employing an integrated local energy decay (ILED) estimate in combination with the Sobolev embedding theorem on a compact Riemannian manifold, we derived $L^\infty$ bounds for the fields. These results were then used to obtain a bound for the conformal energy of the system using the Cauchy-Schwarz inequality and Hardy-type inequalities. |
| title | Uniform Energy Bound for Maxwell-Higgs Equations on Reissner-Nordström Spacetimes |
| topic | Analysis of PDEs General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2410.04724 |