Скачать или смотреть General Relativity - Einstein’s Theory of Gravity : Einstein’s Field Equation

Einstein’s field equation is the basic equation of general relativity. Einstein suspected gravity manifests as curvature of spacetime rather then a force. Physically Einstein’s equation reads as
Spacetime Curvature =(constant)energy-momentum tensor.

There’s three physical motivations behind this equation. First one is General Covariance,in accordance with which laws of physics must be same in all coordinate systems. Second one is Newtonian limit which means this equation reduces to Newtonian gravity when speeds are slow and gravity is weak ,and the third one is Conservation of energy-momentum. In this video you will find the derivation of this field equation starting from the classical Poisson equation of Newtonian theory of gravity.