Numerical study of some solutions to the relativistic equation of scalar particles in the gravitational field of a massive point

A pioneering numerical analysis of some solutions to the relativistic equation for scalar particles in the gravitational field of a massive point source is given. The ground and other states and the corresponding eigenvalues of the discrete spectrum for various values of the momentum of scalar particles are examined. A new feature of the solutions is that their physical characteristics depend on the gravitational mass defect of the point source of the gravitational field. The resulting Sturm–Liouville problem is numerically examined using an algorithm based on a continuous variant of Newton's method. At every iteration step, the corresponding linear boundary value problems are solved by the spline collocation method.