A Wick-rotatable metric is purely electric
Mathematical Physics
2017-03-20 v2 General Relativity and Quantum Cosmology
Differential Geometry
math.MP
Abstract
We show that a metric of arbitrary dimension and signature which allows for a standard Wick-rotation to a Riemannian metric necessarily has a purely electric Riemann and Weyl tensor.
Cite
@article{arxiv.1504.01244,
title = {A Wick-rotatable metric is purely electric},
author = {Christer Helleland and Sigbjorn Hervik},
journal= {arXiv preprint arXiv:1504.01244},
year = {2017}
}
Comments
9 pages, v2:changed and tighten proof. Slightly changed in order to be compatible with the definitions of Wick-rotations in arxiv:1703.04576 [math.DG]