Institute of Theoretical Physics · Faculty of Mathematics and Physics, Charles University
Eur. Phys. J. C 85(5), 537 (2025)
We construct explicit rotating solutions in Einstein's theory of relativity with a minimally coupled free scalar field rederiving and finding solutions in four or five spacetime dimensions. These spacetimes describe, in particular, the back-reaction of a free scalar field evolving in a Kerr spacetime. Adapting the general integrability result obtained many years ago from Eri & scedil;-G & uuml;rses to simpler spherical coordinates, we present a method for rederiving the four-dimensional Bogush-Gal'tsov solution. Furthermore, we find the five-dimensional spacetime featuring a free scalar with two distinct angular momenta. In the static limit, these five-dimensional geometries provide higher-dimensional extensions of the Zipoy-Voorhees spacetime. Last but not least, we obtain the four-dimensional version of a Kerr-Newman-NUT spacetime endowed with a free scalar, where the scalar field's radial profile is extended to incorporate dependence on the polar angular coordinate. Our results offer a comprehensive analysis of several recently proposed four-dimensional static solutions with scalar multipolar hair, representing a unified study of spacetimes with a free scalar field in both four and five dimensions under the general integrability result of Eri¸s–Gürses.
@article{UTF1038,
author = {Barrientos, J. and Charmousis, Ch. and Cisterna, A. and Hassaine, M.},
title = {{Rotating spacetimes with a free scalar field in four and five dimensions}},
journal = {Eur. Phys. J. C},
volume = {85},
number = {5},
pages = {537},
year = {2025},
doi = {10.1140/epjc/s10052-025-14282-y},
eprint = {2501.10223},
archivePrefix = {arXiv},
}