General Relativity/Geodesics

<General Relativity

A geodesic is the generalization of a straight line for curved space. They deal largely with calculus of variations

Metric Geodesics

A metric geodesic is defined as a curve along the shortest or longest possible distance between two points. Mathematically, it is defined as a curve whose length does not change with small variations that vanish at the endpoints. This stability could be a minimum distance, a maximum distance, or a point of inflection.

Mathematically, a metric geodesic is defined by the curve