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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 γ
  3.2.3 Fermi normal coordinates
  3.2.4 Coordinate displacements near γ
  3.2.5 Metric near γ
  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 kα(x)
  3.3.4 Frame components of tensor fields on the world line
  3.3.5 Coordinate displacements near γ
  3.3.6 Metric near γ
  3.3.7 Transformation to angular coordinates
  3.3.8 Specialization to aμ = 0 = Rμν
 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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