Electrostatic system with divergence-free Bach tensor and non-null cosmological constant
Differential Geometry
2022-11-01 v1
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.
Cite
@article{arxiv.2210.16673,
title = {Electrostatic system with divergence-free Bach tensor and non-null cosmological constant},
author = {Benedito Leandro and Róbson Lousa},
journal= {arXiv preprint arXiv:2210.16673},
year = {2022}
}