Energy Conservation at the Gravitational Collapse

Abstract

We apply the principle of energy conservation to the motion of the test particle in gravitational field by requiring that its energy, gained by gravitation, has to be balanced by decrease of its rest mass. Due to the change of mass in gravitational field Newton's force law between gravitating bodies is modified, too. With this modified force law we build up the the classical field theory of gravitation in which all relevant field quantities are in the definition domain $r\in [0,\infty)$ finite and positive. We show that under such circumstances, the energy release at any gravitational collapse is finite. On the other side, the energy conservation leads to an equation which relates the mass change of the test particle due to gravitation and the metric of the corresponding gravitational field. The mass change in Newton's gravitational field lead to a remarkable simple metric which shifts, in contrast to the Schwarzschild metric, the horizon of events to the gravity center of the gravitational collapse.