On the geometry of Petrov type II spacetimes
General Relativity and Quantum Cosmology
2021-07-07 v1 Mathematical Physics
math.MP
Abstract
In general, geometries of Petrov type II do not admit symmetries in terms of Killing vectors or spinors. We introduce a weaker form of Killing equations which do admit solutions. In particular, there is an analog of the Penrose-Walker Killing spinor. Some of its properties, including associated conservation laws, are discussed. Perturbations of Petrov type II Einstein geometries in terms of a complex scalar Debye potential yield complex solutions to the linearized Einstein equations. The complex linearized Weyl tensor is shown to be half Petrov type N. The remaining curvature component on the algebraically special side is reduced to a first order differential operator acting on the potential.
Keywords
Cite
@article{arxiv.2101.00856,
title = {On the geometry of Petrov type II spacetimes},
author = {Steffen Aksteiner and Lars Andersson and Bernardo Araneda and Bernard Whiting},
journal= {arXiv preprint arXiv:2101.00856},
year = {2021}
}