Orthonormal basis in fermi coordinates

[pieas]

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)

 

[maverick_starstrider]

That is impossible to read. Plus, are those d'alembert operators or missing symbol errors?

 

[Entropia]

An orthonormal basis in Fermi coordinates is a set of coordinate basis vectors that are orthogonal to each other and have unit length. These basis vectors are used in the mathematical description of the Fermi coordinates system, which is a coordinate system that is well-suited for describing the motion of particles in a gravitational field.

The properties of an orthonormal basis in Fermi coordinates include:

1. Orthogonality: The basis vectors are perpendicular to each other, meaning that their inner product is equal to zero.

2. Unit length: Each basis vector has a magnitude of 1, making them unit vectors.

3. Co-frame basis: The basis vectors are used to define a co-frame, which is a set of one-forms that can be used to describe the geometry of the space.

4. Compatibility with the Fermi coordinates system: The basis vectors are aligned with the Fermi coordinates axes, making them convenient for describing the motion of particles in a gravitational field.

To solve problems using these basis vectors, you can use their properties to manipulate equations and perform calculations. For example, you can use the orthonormality property to simplify inner products, or use the unit length property to normalize vectors. The values of the basis vectors can be determined from the given equations or can be calculated using the appropriate mathematical formulas.