I Rindler Transformation & 't Hooft's Introduction to General Relativity

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't Hooft's introduction to general relativity includes a derivation of the Rindler transformation, which prompts questions about the formula $$\rho^{-2}g(\zeta)$$ and its implications. The discussion highlights concerns over the use of the "it" convention in the 2010 text. The method for determining acceleration involves analyzing the four-acceleration of an observer in Rindler coordinates, with potential shortcuts available. Additionally, the relationship between time dilation and gravitational potential is questioned, particularly regarding its gradient and implications for gravitational acceleration. Overall, the conversation emphasizes the complexities and nuances in understanding these concepts in general relativity.
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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.

Image1.png


A little bit further he writes

Image2.png


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

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