Towards A Physics-Motivated Small-Velocities Approximation to General Relativity

In the general case, complex non-linear partial differential equations of General Relativity are very hard to solve. Thus, to solve the corresponding physical problems, usually appropriate approximations are used. The first approximation to General Relativity is, of course, Newton’s theory of gravitation. Newton’s theory is applicable when the gravitational field is weak and when all velocities are much smaller than the speed of light. Most existing approximations allow higher velocities, but still limit us to weak gravitational fields. In this paper, he consider the possibility of a different approximation, in which strong fields are allowed but velocities are required to be small. We derive the corresponding equations and speculate on their possible physical consequences. 1 Formulation of the Problem Need for approximations to General Relativity. Since its discovery in 1915 and its first experimental confirmation in 1919, General Relativity has bee