Abstract
The Kerr-Newman metric around charged and rotating sources, as well as Reissner-Nordström and Kerr, included the total mass at infinity, depending on the charge and rotation parameter, and therefore, as solution up to an unknown function of independent parameters, it was only an intermediate stage in solving the problem. The complete solution as a metric with independent parameters was recently given by the author (Zakir, 2022). For a ball with a charge on the surface, the new metrics includes three independent parameters - surface radius, charge, and ball’s gravitational radius, equal to the gravitational radius of neutral matter. The electric field energy exists only outside the ball and contributes to the metric with the same sign as the matter. Therefore, the increase in charge enhances gravity and its effects (time dilation and redshifts, orbit radii and shadows). At collapse of the ball, its surface asymptotically approaches the gravitational radius and the ball freezes (in center’s rest frame), becoming a frozar. Two parameters remain in its metric and the observable consequences are the same as for a ball with a given surface. The metric around frozar with angular momentum is given by a new form of the Kerr metric including two independent parameters - the gravitational radius at the pole and rotation parameter. In it, the contributions to the metric of the energies of matter and rotation have the same sign, and therefore an increase in rotation parameter enhances gravity and its effects. When there is also a charge on the surface, the metric is given by a new form of the Kerr-Newman metric, also including the gravitational radius at the pole as an independent parameter. Its consequences are a combination of the two previous cases. All these consequences are physically correct, but they are opposite to the conclusions from the standard metrics of Reissner-Nordström, Kerr and Kerr-Newman. In these standard metrics, the dependence of the total mass on the charge and rotation parameter was ignored, which led to erroneous predictions about the weakening of effects of gravity at increasing of these parameters. The present article provides a brief review of the new metrics and a more detailed description of their consequences for observable effects.
