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arXiv · 2410.04724

Uniform Energy Bound for Maxwell-Higgs Equations on Reissner-Nordstr\"om Spacetimes

Mulyanto·Ardian N. Atmaja·Fiki T. Akbar·Bobby E. Gunara
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Abstract

In this paper, we prove the uniform energy bound for the Maxwell-Higgs system in the exterior region of Reissner-Nordstr\"om 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.

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Mulyanto, Ardian N. Atmaja, Fiki T. Akbar, Bobby E. Gunara. 2024-10-07. Uniform Energy Bound for Maxwell-Higgs Equations on Reissner-Nordstr\"om Spacetimes. https://arxiv.org/abs/2410.04724

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