publication . Article . Other literature type . 1963

Fermi Normal Coordinates and Some Basic Concepts in Differential Geometry

Manasse, F. K.; Misner, C. W.;
Restricted
  • Published: 01 Jun 1963 Journal: Journal of Mathematical Physics, volume 4, pages 735-745 (issn: 0022-2488, eissn: 1089-7658, Copyright policy)
  • Publisher: AIP Publishing
Abstract
Fermi coordinates, where the metric is rectangular and has vanishing first derivatives at each point of a curve, are constructed in a particular way about a geodesic. This determines an expansion of the metric in powers of proper distance normal to the geodesic, of which the second‐order terms are explicitly computed here in terms of the curvature tensor at the corresponding point on the base geodesic. These terms determine the lowest‐order effects of a gravitational field which can be measured locally by a freely falling observer. An example is provided in the Schwarzschild metric. This discussion of Fermi Normal Coordinate provides numerous examples of the use...
Powered by OpenAIRE Research Graph
Any information missing or wrong?Report an Issue