Year: 2025
Type: article
Abstract: 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 Eriş–Gürses 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 Eriş–Gürses.
Source: The European Physical Journal C
Institutions: University of Tarapacá, Czech Academy of Sciences, Institute of Mathematics, Centre National de la Recherche Scientifique, Université Paris-Saclay, Institut National de Physique Nucléaire et de Physique des Particules, Laboratoire de Physique des 2 Infinis Irène Joliot-Curie, European Organization for Nuclear Research, Charles University, University of Talca
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4410355691