Geodesics have space-time separation {geodesic deviation} along (straight) line perpendicular to geodesics. An equation {equation of geodesic deviation} calculates separation: (D^2)r / Ds^2 + G * r, where D^2 is second partial derivative, r is curvature radius, D is first partial derivative, s is space coordinate, and G is Gaussian curvature. In empty space-time, geodesics are parallel straight lines. Empty space-time has no curvature, so r is zero, and geodesic deviation is zero.
Physical Sciences>Physics>Relativity>General Relativity>Equations
5-Physics-Relativity-General Relativity-Equations
Outline of Knowledge Database Home Page
Description of Outline of Knowledge Database
Date Modified: 2022.0224