Undergrad Finding Most General Form of Rindler Coordinates

[kent davidge]

I'm searching, but so far I have not found a derivation of the coordinates shown by wikipedia in the very beginning of https://en.wikipedia.org/wiki/Rindler_coordinates#Characteristics_of_the_Rindler_frame.

It seems obvious from the relation $X^2 - T^2 = 1 / a^2$, ($c = 1$), that $X = (1/a) \cosh \varphi$ and $Y = (1/a) \sinh \varphi$, but that $\varphi = t/a$ is not obvious.

Sorry, I've titled this thread as "the most general form" but later realized that the form I'm talking about is not the most general form. Anyways the question remains.

 

[PeterDonis]

that $\varphi = t/a$ is not obvious.

It shouldn't be, since it's wrong. As you've defined $\varphi$, it should be $\varphi = a t$, where $t$ is the proper time along the worldline.

 

[kent davidge]

It shouldn't be, since it's wrong. As you've defined $\varphi$, it should be $\varphi = a t$, where $t$ is the proper time along the worldline.

Yes, I typed it wrong.

 

[Orodruin]

Did you try computing the proper time along the worldline of a Rindler-stationary observer? If so, what did you get?

 

[kent davidge]

Did you try computing the proper time along the worldline of a Rindler-stationary observer? If so, what did you get?

Thanks. Got it after your hint.