Spacetimes with a separable Klein-Gordon equation in higher dimensions
Abstract
We study spacetimes that lead to a separable Klein-Gordon equation in a general dimension. We introduce an ansatz for the metric in higher dimensions motivated by analogical work by Carter in four dimensions and find solutions of the Klein-Gordon equation. For such a metric we solve the Einstein equations and regain the Kerr-NUT-(A)dS spacetime as one of our results. Other solutions lead to the Einstein-K\"ahler metric of a Euclidean signature. Next we investigate a warped geometry of two Klein-Gordon separable spaces with a properly chosen warped factor. We show that the resulting metric leads also to a separable Klein--Gordon equation and we find the corresponding solutions. Finally, we solve the Einstein equations for the warped geometry and obtain new solutions.
Cite
@article{arxiv.1509.01667,
title = {Spacetimes with a separable Klein-Gordon equation in higher dimensions},
author = {Ivan Kolar and Pavel Krtous},
journal= {arXiv preprint arXiv:1509.01667},
year = {2016}
}
Comments
12 pages, no figures