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Area-charge inequality and local rigidity in charged initial data sets

Area-charge inequality and local rigidity in charged initial data sets

来源:Arxiv_logoArxiv
英文摘要

This paper investigates the geometric consequences of equality in area-charge inequalities for spherical minimal surfaces and, more generally, for marginally outer trapped surfaces (MOTS), within the framework of the Einstein-Maxwell equations. We show that, under appropriate energy and curvature conditions, saturation of the inequality $\mathcal{A} \geq 4\pi(\mathcal{Q}_{\rm E}^2 + \mathcal{Q}_{\rm M}^2)$ imposes a rigid geometric structure in a neighborhood of the surface. In particular, the electric and magnetic fields must be normal to the foliation, and the local geometry is isometric to a Riemannian product. We establish two main rigidity theorems: one in the time-symmetric case and another for initial data sets that are not necessarily time-symmetric. In both cases, equality in the area-charge bound leads to a precise characterization of the intrinsic and extrinsic geometry of the initial data near the critical surface.

Abra?o Mendes

物理学

Abra?o Mendes.Area-charge inequality and local rigidity in charged initial data sets[EB/OL].(2025-05-26)[2025-07-16].https://arxiv.org/abs/2505.20060.点此复制

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