Orthonormal basis in fermi coordinates

pieas
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please help in this problem
what are these basis and what are there there properties.how i can i put there values to solve my problems.
ˆB
= (
1
2
 + +)er
er
+ (
1
2
 − +)e
e
+ (× + !)er
e
+ (× − !)e
er
. (4.13)
where eµ
are co-frame basis satisfying eµ
E
 = µ
 . The ESR can be extracted from the
evolution tensor (4.13) using the basis vectors as follows,
 = ˆB ˆh ≡ ˆB
, (4.14)
+ =
1
2
( ˆB E
r E
r − ˆB E
 E
 ), (4.15)
× =
1
2
( ˆB E
r E
 + ˆB E
 E
r ), (4.16)
! =
1
2
( ˆB E
r E
 − ˆB E
 E
r ). (4.17)
 
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