Part II
Coordinate Systems

8 Riemann normal coordinates
 8.1 Definition and coordinate transformation
 8.2 Metric near x′
9 Fermi normal coordinates
 9.1 Fermi–Walker transport
 9.2 Tetrad and dual tetrad on γ
 9.3 Fermi normal coordinates
 9.4 Coordinate displacements near γ
 9.5 Metric near γ
 9.6 Thorne–Hartle–Zhang coordinates
10 Retarded coordinates
 10.1 Geometrical elements
 10.2 Definition of the retarded coordinates
 10.3 The scalar field r(x ) and the vector field α k (x )
 10.4 Frame components of tensor fields on the world line
 10.5 Coordinate displacements near γ
 10.6 Metric near γ
 10.7 Transformation to angular coordinates
 10.8 Specialization to a μ = 0 = R μν
11 Transformation between Fermi and retarded coordinates; advanced point
 11.1 From retarded to Fermi coordinates
 11.2 From Fermi to retarded coordinates
 11.3 Transformation of the tetrads at x
 11.4 Advanced point

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