On the Theory and Observation of Highly Collapsed Stars

The investigation presented here falls into two parts. In the first part (Sections A to H) the general relativistic solution given by Schwarzschild of the problem of a homogeneous sphere of constant density is discussed. For every given density a characteristic mass $M_l$ exists, for which the pressure in the center of the sphere becomes infinite, and for which the velocity of light in the same point becomes equal to zero. In the case of collapsed neutron stars. $M_l$ is of the order of a large stellar mass. The effective mass and the gravitational energy of the sphere are determined as functions of its proper mass. Equations are developed which express the velocity and the wave-length of light as functions of the distance from the center of the sphere. The characteristic mass $M_l$ of collapsed neutron stars is expressed in terms of the charge and mass of the electron and the proton and the universal gravitational constant. Some possible relations of the results obtained with recent cosmological theories are pointed out.