SR can handle accelerated system but not gravity(fictitious force):
a,
b,
Jacobian/Basis Vector. We can think of Basis vector as tangent vector to path with parameter of t.
It’s all about converting between the two frames:
Covariant Derivative in Flat Spacetime (Rindler Coordinates)
The concept of Rindler Cordinates is still bit of rusty:
Naixian Zhang 