**Abstract**

The Kerr metric, the external metric for a rotating body, contains the equatorial gravitational radius implicitly depending on the specific angular momentum (SAM). Ignoring this dependence due to the formal mathematical approach without understanding the physical aspects led to absurd unphysical consequences in the black hole theory, in particular, that an increase in the rotational energy at increasing SAM weakens gravity, decreasing the gravitational radius at the pole and the effects of gravity (redshifts, mean radii of orbits and shadows). This shortcoming of the Kerr metric is improved in a new form of this metric with an independent parameter - the gravitational radius at the pole, determined by the mass of matter without rotational energy. The contributions of the energies of matter and rotation have the same sign and an increase in SAM strengthens gravity, increasing its effects (the equatorial gravitational radius, redshifts, mean radii of orbits and shadows). The modified form of the Kerr metric describes the gravitational field of a frozar having angular momentum, a star with frozen structure and the surface asymptotically tending to the local gravitational radius (minimal at pole and maximal at equator). The application of this method to the Kerr-Newman metric, including the charge, and to the NUT metric, gave modified forms of these metrics with independent parameters. In the frozar theory, particle energies are positive everywhere, and the theory is free from the non-physical effects of the former black hole theory (horizons, singularities, ergosphere and the extraction of energy from it, evaporation). Thermodynamics of frozars follows from the almost irreversible freezing, as the result of which, during accretion and other processes, the mass of neutral matter without rotational energy grows almost irreversibly.