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3 Coordinate Systems


 3.1 Riemann normal coordinates
  3.1.1 Definition and coordinate transformation
  3.1.2 Metric near x'
 3.2 Fermi normal coordinates
  3.2.1 Fermi-Walker transport
  3.2.2 Tetrad and dual tetrad on g
  3.2.3 Fermi normal coordinates
  3.2.4 Coordinate displacements near g
  3.2.5 Metric near g
  3.2.6 Thorne-Hartle coordinates
 3.3 Retarded coordinates
  3.3.1 Geometrical elements
  3.3.2 Definition of the retarded coordinates
  3.3.3 The scalar field r(x) and the vector field a k (x)
  3.3.4 Frame components of tensor fields on the world line
  3.3.5 Coordinate displacements near g
  3.3.6 Metric near g
  3.3.7 Transformation to angular coordinates
  3.3.8 Specialization to am = 0 = Rmn
 3.4 Transformation between Fermi and retarded coordinates; advanced point
  3.4.1 From retarded to Fermi coordinates
  3.4.2 From Fermi to retarded coordinates
  3.4.3 Transformation of the tetrads at x
  3.4.4 Advanced point


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