Discontinuity of First Derivatives of Metric Tensor and Mach's Principle

Abstract

A static massive thin spherical shell in a universe empty, except for the shell, is con­ structed which provides suitable boundary conditions that enforce Mach's principle in general relativity. The momentum-energy tensor of the surface distribution on the shell is given by the terms containing a-function, that appear in Einstein's field equations if the first derivatives of the metric tensor are discontinuous across the interface of the two adjacent regions. Einstein's field equations, in this case are constructed from the metric tensor which is a linear combina­ tion of two metric tensors specifying two adjacent regions, making use of the step-function. This method of constructing the field equation is the same as has been followed by Nariai.