[Mentors note: this thread was split off from an older discussion of Rindler coordinates] Can somebody help me understand why acceleration along the hyperbola is constant? To be more precise: assume (X,T) is the inertial coordinates and (x,t) the corresponding Rindler transformations. x=Xcosh(aTc ) t=Xc sinh(aTc ) A uniformly accelerated frame moves along the curves with constant x. What do we men by fixed acceleration here? is it second derivative of x relative to t? if x is constant then its first and second derivatives are of course zero. The second derivative of X relative to T cannot be a constant either, because that would imply a parabolic and not hyperbolic path with no limit on speed of light. The only possibility that I can see is second derivative of X relative to t. is that indeed what we mean by constant acceleration along the hyperbola? And if so how can one prove that it is constant (equal to a)?