Electrostatic system with divergence-free Bach tensor and non-null cosmological constant
arXiv:2210.16673 · doi:10.1515/forum-2023-0040
Abstract
We prove that three-dimensional electrostatic manifolds with divergence-free Bach tensor are locally conformally flat, provide that the electric field and the gradient of the lapse function are linearly dependent. Consequently, a three-dimensional electrostatic manifold admits a local warped product structure with a one-dimensional base and a constant curvature surface fiber.
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