Weyl-type solutions with multipolar scalar fields

TL;DR

This paper develops a method to generate and analyze Weyl-type solutions with multipolar scalar fields in higher-dimensional Einstein gravity, including solutions with magnetic and scalar fields.

Contribution

It introduces a procedure to generate scalar multipolar fields and solutions with magnetic fields, extending known solutions like Schwarzschild--Melvin and Fisher--Janis--Newman--Winicour.

Findings

Generated solutions include scalar and magnetic field counterparts of known spacetimes.

The method exploits $SO(2)$ symmetry and Harrison-type transformations.

New solutions encompass limits such as Schwarzschild--Melvin with scalar and magnetic fields.

Abstract

A class of solutions in $d$-dimensional Einstein gravity minimally coupled to a massless scalar field is studied, where the spacetime metric is of a generalized Weyl form with $d-2$ commuting Killing vectors. In addition to the procedure to generate scalar multipolar fields, a $SO(2)$ symmetry can be exploited to generate further solutions. A particular result of this procedure is a solution that contains the scalar counterpart of the Schwarzschild--Melvin and the Fisher--Janis--Newman--Winicour solutions as particular limits. Furthermore, a Harrison-type transformation can also be performed to generate solutions with magnetic fields. Using this transformation we obtain a solution with magnetic and scalar fields present and contains both magnetic and scalar counterparts of Schwarzschild--Melvin as limits.