In General Relativity, these are the curves that **a free particle** (that is, a particle upon which no force acts, where ‘force’ in this case excludes gravity, since the effects of gravity are felt entirely through the curvature of space-time) **will follow in a curved space-time **.

A geodesic could be equivalently defined as:

- a line which generalizes the notion of a "
**straight line**" to curved spacetime. From this perspective, we have been through the way to derive the geodesic equation directly from the Equivalence Principle in Geodesic equation and Christoffel symbols. - a time-like wordline that
**maximizes the Proper Time**(E*igenZeit*) between two given events^{[1]}. See our article Geodesic equation from the principle of least action for the full derivation. - a line that
**parallel transports its tangent vector along itself**. See Geodesics from covariant derivative for the full derivation.

[1] Refer to our article Geodesics as proper time maximization to see how this applies also in Special Relativity.