Relativistic energy and mass in the weak field limit

Abstract

Within the framework of the covariant theory of gravitation (CTG), the energy is calculated for a system with continuously distributed matter, taking into account the contribution of the gravitational and electromagnetic fields and the contribution of the pressure and acceleration fields. The total energy of all the fields is equal to zero, and the system's energy is formed from the energy of the particles, which are under the influence of these fields. From the expression for the energy, the inertial M and gravitational mg masses of the system are found. These masses are compared with mass mb, obtained by integrating the density over the volume, and with the total mass m' of the body particles scattered to infinity in order to make the energy of macroscopic fundamental fields equal to zero. The ratio for the masses is obtained: m' = M < mb = mg. From this the possibility of non-radiative ideal spherical collapse follows, when the system's mass M does not change during the collapse. In addition, the mass of the system is less than the gravitational mass. In contrast, in the general theory of relativity (GTR), the ratio for masses is obtained in a different form: M = mg < mb < m'. In CTG, the electromagnetic field energy reduces the gravitational mass; whereas in GTR, on the contrary, the electromagnetic field energy increases the gravitational mass. In order to verify the obtained results, it is suggested to conduct an experiment on measuring the change of the gravitational mass of the body with increasing its electrical charge.