arXiv subjects

Róbson Lousa

Publications and source records attributed to Róbson Lousa.

3 recordsLinked to original sources

arXiv2026

Notes on a Cotton-type tensor for electrostatic systems

We introduce a natural (0,3)-tensor associated with electrostatic systems in arbitrary dimensions. This tensor arises from the comparison between the Cotton and Weyl decompositions of the Riemann curvature tensor and extends several identities previously known in dimensions three and four. We prove that it is totally trace-free and satisfies the same algebraic symmetries as the Cotton tensor. We further investigate its behavior under the natural assumption that the electric field is collinear with the gradient of the lapse function, obtaining a simplified expression. Along the way, we extend a boundary collinearity result to arbitrary dimensions and derive several identities that may be useful in the study of electrostatic systems.

math.DG↗

arXiv2022

Electrostatic system with divergence-free Bach tensor and non-null cosmological constant

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.

math.DG↗

arXiv2021

On the geometry of electrovacuum spaces in higher dimensions

A classical question in general relativity is about the classification of regular static black hole solutions of the static Einstein-Maxwell equations (or electrovacuum system). In this paper, we prove some classification results for an electrovacuum system such that the electric potential is a smooth function of the lapse function. In particular, we show that an n-dimensional locally conformally flat extremal electrovacuum space must be in the Majumdar-Papapetrou class. Also, we prove that any three or four dimensional extremal electrovacuum space must be locally conformally flat. Moreover, we prove that an n-dimensional subextremal electrovacuum space with fourth-order divergence free Weyl tensor and zero radial Weyl curvature such that the electric potential is in the Reissner-Nordström class is locally a warped product manifold with (n-1)-dimensional Einstein fibers. Finally, a three dimensional subextremal electrovacuum space with third-order divergence free Cotton tensor was also classified.

gr-qc↗