 Fermi–Walker transport

Transport defining a nonrotating frame along an accelerated timelike curve. With four-velocity normalization $u^{\mu }{u}_{\mu }=-c^2$ and four-acceleration $a^{\mu }=D{u}^{\mu }/d\tau$, the displayed equation preserves inner products and keeps a spatial spin orthogonal to $u$. Along a geodesic, $a^{\mu }=0$ and it reduces to parallel transport.

Fermi-Walker transport is a concept in general relativity that describes how vectors (such as four-vectors) are transported along a curve in a curved spacetime. It is particularly useful in the context of allowing a parallel transport of vectors along a worldline in a way that respects the geometry of spacetime. The method is named after physicist Enrico Fermi and is often associated with the study of accelerated motion in general relativity.