Towards the rotating scalar-vacuum black holes

Abstract

The problem of merging in black holes the rotation and a massless scalar field is treated. It is argued in the comment that the Kerr-like and Demianski-like metrics in General Relativity with a free massless scalar field or in the free Brans-Dicke theory, claimed so far in the literature as an application of the Newman-Janis algorithm, prove to be invalid. Finding the missing stationary axisymmetric scalar-vacuum solution(s), containing the Kerr one, is still urgent.