How to Wick rotate generic curved spacetime
Abstract
It is an article of folklore that the collection of ideas identified as Euclidean quantum gravity may be derived from ordinary Lorentzian signature gravity by the procedure of Wick rotation. This note will attempt to shed some light on this relatively ill-understood procedure. I argue that it proves inappropriate and unhelpful to regard Wick rotation in terms of a complex deformation of the time coordinate. Rather, Wick rotation can more usefully be viewed as a complex deformation of the spacetime metric. This simple reformulation of the Wick rotation procedure, while it leaves flat space physics unaffected, has profound implications for quantum gravity.
Keywords
Cite
@article{arxiv.1702.05572,
title = {How to Wick rotate generic curved spacetime},
author = {Matt Visser},
journal= {arXiv preprint arXiv:1702.05572},
year = {2017}
}
Comments
V1: 11 pages. Old pre-arXiv essay originally written for the 1991 Gravity Research Foundation essay contest. For many years a PDF copy of the essay was available at the GRF website, but many of the older essays have now been removed from that website. Apart from purely cosmetic issues, this arXiv upload is an accurate reflection of that 1991 essay. V2: Extra historical comments; 6 references added