New method to generate exact scalar-tensor solutions

摘要

A new method is proposed, that establishes a one to one correspondance between the whole set of static axially symmetric vacuum general relativity solutions and a specific class of stationary axially symmetric scalar-Einstein (R_(ab) = ?_aΦ?_bΦ) solutions for any mass and angular momentum. The method explicitly takes advantage of the Kerr metric Ricci flatness. This also results in a class of stationary axially symmetric vacuum, ie Kerrlike, Brans-Dicke solutions. A particular solution, that is asymptotically flat, is more closely considered. It converges to Kerr for a vanishing scalar charge, but fails to converge to the Fisher- Janis-Newman-Winicour solution for a vanishing “rotation parameter.” This solution exhibits a set of singular points, with a naked subset having a ringlike structure.