https://doi.org/10.1140/epjc/s10052-025-14282-y
Regular Article -Theoretical Physics
Rotating spacetimes with a free scalar field in four and five dimensions
1
Sede Esmeralda, Universidad de Tarapacá, Avenida Luis Emilio Recabarren 2477, Iquique, Chile
2
Institute of Mathematics of the Czech Academy of Sciences, Žitná 25, 115 67, Praha 1, Czech Republic
3
Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405, Orsay, France
4
Theoretical Physics Department, CERN, 1211, Geneva 23, Switzerland
5
Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, 180 00, Praha 8, Czech Republic
6
Instituto de Matemáticas, Universidad de Talca, Casilla 747, Talca, Chile
a
jbarrientos@academicos.uta.cl
Received:
3
April
2025
Accepted:
4
May
2025
Published online:
14
May
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 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.
© The Author(s) 2025
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