Surface Layer in General Relativity and Integral Form of Field Law

TL;DR: In this paper, the field equations and boundary conditions for a surface layer can be deduced from an integral flux law, and the theory of surface layer in general relativity is then worked out.

Abstract: Assuming that the metric tensor gij depends on a continuous parameter e, we write Einstein's field equations of general relativity in the form of a divergence equation. The theory of surface layer in general relativity is then worked out. Finally, an integral flux law is proposed from which both the field equations and the boundary conditions for a surface layer can be deduced.