Metrics with irreducible mass leading to a correct parameter dependence of gravitational effects around charged and rotating bodies

Abstract

The standard metrics outside of charged and rotating sources (Kerr-Newman in general, Reissner-Nordström and Kerr in particular) contain the total mass at infinity, which includes both the mass of a neutral non-rotating body and the mass equivalents of rotational and electric field energies. Therefore, the total mass is related to other parameters of the metric - angular momentum and charge. However, at studying the dependence of gravitational effects on parameters, this relationship was ignored, assuming total mass to be constant at varying angular momentum and charge. This error led to physically absurd predictions about the weakening of gravity and its effects with increasing the rotational and electric field energies. To eliminate such errors, the total mass must be expressed in terms of independent parameters - the mass of the neutral non-rotating matter of the source, charge and angular momentum. Recently this has been done using as an independent parameter the mass determined from the gravitational radius at the pole when the charge is only on the surface (Zakir, 2022). In the present paper it is used “irreducible mass”, earlier defined heuristically as the remainder of total mass after the removal of angular momentum and charge. Earlier, mass formulas expressing total mass in terms of irreducible mass were proposed by Florides (1960) (improved by the author (2022)) for charged bodies and then by Christodolou (1970) for rotating and Christodolou-Ruffini (1971) for charged rotating sources. In the paper, the standard metrics are transformed to metrics with independent parameters by substituting the expression for the total mass according to these mass formulas. It is shown that the metrics in this form lead to a physically correct dependence of the effects of gravity on the parameters, in particular, the growth of the rotation and electric field energies strengthens gravity and its effects, such as time dilation and redshifts, increases radii of orbits and the area of shadow.