Theoretical motivation for general relativity

A theoretical motivation for general relativity, including the motivation for the geodesic equation and the Einstein field equation, can be obtained from special relativity by examining the dynamics of particles in circular orbits about the Earth. A key advantage in examining circular orbits is that it is possible to know the solution of the Einstein Field Equation a priori. This provides a means to inform and verify the formalism.

General relativity addresses two questions:

1. How does the curvature of spacetime affect the motion of matter?
2. How does the presence of matter affect the curvature of spacetime?

The former question is answered with the geodesic equation. The second question is answered with the Einstein field equation. The geodesic equation and the field equation are related through a principle of least action. The motivation for the geodesic equation is provided in the section Geodesic equation for circular orbits. The motivation for the Einstein field equation is provided in the section Stress–energy tensor.

General relativity
${\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={\kappa }T_{\mu \nu }}$
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