Normal frames for non-Riemannian connections

The principal properties of geodesic normal coordinates are the vanishing of the connection components and first derivatives of the metric components at some point. It is well-known that these hold only at points where the connection has vanishing torsion and nonmetricity. However, it is shown that normal frames, possessing the essential features of normal coordinates, can still be constructed when the connection is non-Riemannian. Submitted to Class. Quantum Grav. Date: 4 February 2008 † Email: [email protected] ‡ Postal address: GMD–SCAI, D–53754 St Augustin, Germany