APPENDIX B
 THE GEOMETRY OF FERMI NORMAL COORDINATES
 In Step (ii) of Subsection 4.3.3 we obtained the expressions of Fermi normal
coordinates in terms of the static inertial coordinates XA as



TFN = -UA A + ABCDXBXCXD + A BCDEXB_ D + O(X5/R4),

 (Bl)

 FXN o' [XA + B, BXCX X+ A, BCDEoXXXX] + O(X/i(),
 (B2)
where I 1, 2, 3 and

 SA -- A T P ,Q CR i3 Q B R c hPD + 3 TR hPchQQ
 BCD 6 Q R (BB C RD R 3QB^ RCl D R3WBI Cl D

 +hPBhQchRD), (B3)


 BCD 24 PQRS Bo Q r C( crRDn S + 4 RTTc' Dr EShPz

 +67RBrSchPDhQE + 47RBhPchQDhRE

 +hPBhQchRDhSE), (B4)

with

 7AB UoB,( (B5)

 hAB =- A (I)B AB U UB. (B6)


 The transformation via Eqs. (Bl) and (B2) reproduces the desired geome-
try of Fermi normal coordinates. One can verify this by examining the metric