Effects of gravity around charged and rotating collapsars in metrics with independent parameters

Abstract

The external metric of the ball with a charge on the surface, as a solution to the Einstein-Maxwell equations, depends on three independent parameters - the surface radius, the charge and the gravitational radius of the ball, which is equal to the gravitational radius of a neutral non-rotating matter. The electric field exists only outside the ball, and its energy contributes to the metric with the same sign as the matter. Therefore, an increase in charge enhances gravity, increasing the magnitude of its effects (redshifts, orbital radii and shadows, etc.). The metric outside the spherical collapsar follows from the metric of the ball as the surface asymptotically approaches the gravitational radius and therefore includes two parameters instead of three, and its observable consequences are the same as for a ball with a given surface radius. The metric outside such a collapsar during its rotation also includes the rotation parameter as an independent parameter. The new form of the Kerr-Newman metric also includes an independent parameter - the gravitational radius at the pole. In it, the contributions to the metric of the energies of matter and rotation have the same sign, and an increase in the rotation parameter also enhances gravity, increasing the magnitude of its effects (gravitational radius at the equator, redshifts, average radii of orbits and shadows). These consequences are physically correct, but they are inverse to the previous non-physical predictions based on the standard Reisner-Nordström, Kerr and Kerr-Newman metrics. The latter included the total mass at infinity depending on the charge and/or rotation parameter, and predictions were made without taking this dependence into account, which led to the erroneous conclusion that an increase in charge and/or rotation parameter weakens gravity, reducing the magnitude of its observed effects.