# What happens if the moving frame in special relativity is non-inertial?

We have the lorentz transformation equations for relating inertial frame of references.

What will the transformation equations be if the frames are non inertial?

Is there any "pseudo-force like thing" in special relativity?

• Three distinct questions here with three distinct answers. – dmckee Jul 1 '18 at 20:10
• Sorry,now I have edited the question. – Man_57 Jul 1 '18 at 20:18
• Not to be snarky with you, but you have read through this: en.wikipedia.org/wiki/Non-inertial_reference_frame ? – user198207 Jul 1 '18 at 20:26
• For a linear acceleration: en.m.wikipedia.org/wiki/Rindler_coordinates ; For non-zero y and z speeds, still Special Relativity (search for General Lorentz Transformation or Poincare Symmetry); for rotation you may need to use General Relativity. Fictitios forces are gravity in non inertial frames according to the equivalence principle. – safesphere Jul 1 '18 at 21:01

You choose as stationary frame an inertial frame (in which SR assumptions hold) and then you measure the non inertial frame with the Lorentz transformation, however with the relative velocity $v$ and the Lorentz factor $\gamma$ referring to the inertial reference frame at each instant in time at rest with the accelerated frame.
• It is not a theory on top of SR. Simply you track the accelerated frame in that way. As for the mathematics, it is the Lorentz transformation. Of course, the velocity $v$ and the Lorentz factor $\gamma$ will vary at each instant in time. – Michele Grosso Jul 2 '18 at 17:03