An alternative to the Simon tensor. (1st July 2021)

• Record Type: Journal Article
• Authors: Nozawa, Masato
• Is Part Of: Classical and quantum gravity. Volume 38:Number 15(2021)
• Publication Date: 2021-07-01
• Subjects: black hole -- exact solution -- Ernst system; Quantum gravity -- Periodicals; Gravitation -- Periodicals; Relativity (Physics) -- Periodicals; Space and time -- Periodicals; Periodicals; 521.1
• DOI: 10.1088/1361-6382/ac0a87
• Languages: English
• ISSNs: 0264-9381

Abstract

Abstract: The Simon tensor gives rise to a local characterization of the Kerr-NUT family in the stationary class of vacuum spacetimes. We find that a symmetric and traceless tensor in the quotient space of the stationary Killing trajectory offers a useful alternative to the Simon tensor. Our tensor is distinct from the spatial dual of the Simon tensor and illustrates the geometric property of the three dimensional quotient space more manifest. The reconstruction procedure of the metric for which the generalized Simon tensor vanishes is spelled out in detail. We give a four dimensional description of this tensor in terms of the Coulomb part of the imaginary selfdual Weyl tensor, which corresponds to the generalization of the three-index tensor defined by Mars. This allows us to establish a new and simple criterion for the Kerr-NUT family: the gradient of the Ernst potential becomes the non-null eigenvector of the Coulomb part of the imaginary selfdual Weyl tensor. We also discuss the SU(1, 2) covariant extension of the obstruction tensor into the Einstein–Maxwell system as an intrinsic characterization of the Kerr–Newman-NUT family.