Undergrad 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".
 

Thread 'Question about Parallel Transport'

In this video I can see a person walking around lines of curvature on a sphere with an arrow strapped to his waist. His task is to keep the arrow pointed in the same direction How does he do this ? Does he use a reference point like the stars? (that only move very slowly) If that is how he keeps the arrow pointing in the same direction, is that equivalent to saying that he orients the arrow wrt the 3d space that the sphere is embedded in? So ,although one refers to intrinsic curvature...
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