Physically consistent metrics with independent parameters instead of standard metrics with unphysical consequences. 1. Charged sources

Abstract

The metric around a ball with a surface charge, obtained from the Einstein-Maxwell equations, has three independent parameters – the charge, surface radius and the ball’s gravitational radius, equal to the gravitational radius of the matter. The electric field energy there is only outside the ball and contributes to the metric with the same sign as matter. Therefore, an increase in charge enhances the effects of gravity, increasing the radii of orbits and shadows, redshifts and deflection angles. At the collapse, in the rest frame of the center, the surface freezes above the ball’s gravitational radius, and the inner layers freeze above the gravitational radius of the matter inside them, i.e. the collapsed ball becomes not a black hole, but a frozar, an object with a gravitationally frozen structure. The frozar’s metric follows from the ball’s metric as its surface tends to the gravitational radius and thus contains two parameters instead of three. The frozar’s charge is located over the gravitational radius and its total mass, as for the ball, is finite. Observable consequences of the frozar metric are the same as for the ball. On the contrary, in the black hole theory, the Reissner-Nordström metric contains the total mass at infinity, which depends on the charge and diverges, since it includes the energy of the electric field diverging for a point charge. To ignore this divergence, the total mass was renormalized and replaced with the “observable” mass. Then, already by mistake, the dependence of the total mass on charge was missed. The result of this double disregard was a number of unphysical consequences, inverse to the case of the ball, which complicated the physical picture. It was argued that there are two horizons and the increase in charge weakens the gravity by decreasing the gravitational radius and observable effects of gravity, such as redshifts, radii of orbits and shadows, i.e. it was seriously stated that the positive energy of the electric field antigravitates, which is physically absurd.

Shadow area growth with increasing of charge and angular momentum in the Kerr-Newman metric with irreducible mass

“…The standard Kerr-Newman (KN) metric outside a charged rotating body contains its total mass M , determined from the transition to the Schwarzschild metric at r . In the equatorial plane /2   (in Boyer-Lindquist coordinates) it has the form (notations and references see in [1,2]):…”

“…Various definitions of the dependence of M on a and Q are possible, differing in model assumptions about the source and its environment [1][2][3][4][5][6]. The well-known one, which has become generally accepted, is the Christodolou-Ruffini (CR) mass formula [3,4]:…”

“…Although the CR formula (2) was obtained using hypothetical methods for extracting the rotational energy of a body, nevertheless, qualitatively the course of the dependence M on the other two parameters is conveyed correctly by it, and the small differences from other mass formulas in taking into account the rotational energy are purely quantitative and quite small [1,2,6].…”

“…In the present letter, where the parametric dependence of the contour of the shadow of a charged rotating source is studied, this form of the KN metric will be used. A more detailed description and discussion will be given in [1,2]. Here only the final formula for the shadow contour and the resulting figures in the standard (1) and new (4) forms of the KN metric will be presented.…”

“…A more detailed description of the consequences of metrics with independent parameters and their further applications will be given in the article [1] and in the book [2].…”