Rotating spacetimes with a free scalar field in four and five dimensions

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.

V2 matches published version in EPJC (published on 14 May)

References in corpus (10)

• Healthy theories beyond Horndeski
• Exploring gravitational theories beyond Horndeski
• Charging axisymmetric space-times with cosmological constant
• The non-integrability of the Zipoy-Voorhees metric
• Stationary axisymmetric spacetimes with a conformally coupled scalar field
• Revisiting Buchdahl transformations: New static and rotating black holes in vacuum, double copy, and hairy extensions
• Three parameter metrics in the presence of a scalar field in four and higher dimensions
• A class of rotating metrics in the presence of a scalar field
• A class of Taub-NUT-scalar metrics via Ehlers transformations
• Nonspherically-symmetric black hole in Einstein-massless scalar theory

Cited by in corpus (5)

• A class of charged and charged-Taub-NUT metrics in the presence of a massless scalar field and some of their astrophysical aspects
• Generation of gravitating solutions with Baryonic charge from Einstein-Scalar-Maxwell seeds
• Weyl-type solutions with multipolar scalar fields
• Dynamical axisymmetric compact objects in General Relativity
• Revisiting a family of five-dimensional charged, rotating black holes