In the mathematical theory of Riemannian geometry, there are two uses of the term Fermi coordinates. In one use they are local coordinates that are adapted to a geodesic. In a second, more general one, they are local coordinates that are adapted to any world line, even not geodesical.

making use of Fermi–Walker's transport and is non-rotated (in a precise sense related to the decomposition of Lorentz transformations into pure transformations and rotations) with respect to the initial basis, this is the physical meaning of Fermi–Walker's transport.

exists.

, all Christoffel symbols is not a geodesic. Such coordinates are called Fermi coordinates and are named after the Italian physicist Enrico Fermi who first constructed them when he was twenty-one. The above properties are only valid on the geodesic. The Fermi-coordinates adapted to a null geodesic is provided by Mattias Blau, Denis Frank, and Sebastian Weiss.

In the Riemannian case at least, Fermi coordinates can be generalized to an arbitrary submanifold.

See also

• Proper reference frame (flat spacetime)#Proper coordinates or Fermi coordinates

• Geodesic normal coordinates

• Fermi–Walker transport

• Christoffel symbols

• Isothermal coordinates

References