A Family of Inertial Observers
The frame field
represents the local Lorentz frame defined by a family of nonspinning inertial observers. That is,
which means that the integral curves of the timelike unit vector field are timelike geodesics, and also
which means that the spacelike unit vector fields are nonspinning. (They are Fermi-Walker transported.) Here, is a timelike unit vector field, while are spacelike unit vector fields.
Nonspinning inertial frames are as close as we can come in curved spacetimes to the usual Lorentz frames known from special relativity, where Lorentz transformations are simply changes from one Lorentz frame to another.
Read more about this topic: Monochromatic Electromagnetic Plane Wave
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