Deriving the factor ρ^−2g(ζ) in 't Hooft's Rindler transformation

[wnvl2]

I am reading 't Hooft introduction to general relativity.

https://webspace.science.uu.nl/~hooft10 ... l_2010.pdf

In this text 't Hoof derives the Rindler transformation.

A little bit further he writes

My question is, how does he come to that formula $$\rho^{-2}g(\zeta)$$

 

[Ibix]

Gentle shudder at the use of $it$ convention. Did he really do that in 2010? Ugh.

The general way of getting the acceleration is to take the modulus of the four-acceleration of the observer who is stationary in Rindler coordinates. There are possible shortcuts in this case, though. Has he established a relationship between time dilation and gravitational potential? If so you can take its gradient to get the acceleration due to "gravity".