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 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.
Yen-Kheng Lim (Thu,) studied this question.
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