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

In summary, 't Hooft's text introduces the concept of the Rindler transformation and discusses the formula $$\rho^{-2}g(\zeta)$$ which can be derived through various methods including taking the modulus of the four-acceleration of an observer in Rindler coordinates. The use of the "it" convention and the possible shortcuts in obtaining acceleration are also mentioned. The relationship between time dilation and gravitational potential is also discussed.
  • #1
wnvl2
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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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  • #2
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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1. What is the Rindler transformation in general relativity?

The Rindler transformation is a coordinate transformation used to describe the motion of an observer in a uniformly accelerating reference frame. It is commonly used in the study of black holes and is an important tool in understanding the effects of gravity on objects.

2. How does the Rindler transformation relate to 't Hooft's introduction to general relativity?

't Hooft's introduction to general relativity discusses the Rindler transformation as a way to understand the effects of gravity in curved spacetime. It is used to derive the equations of motion for objects in a gravitational field and provides a useful conceptual framework for understanding general relativity.

3. What are the main concepts covered in 't Hooft's introduction to general relativity?

The main concepts covered in 't Hooft's introduction to general relativity include the principles of general relativity, the Rindler transformation, the equivalence principle, the geodesic equation, and the Einstein field equations. It also covers the basics of curved spacetime and the effects of gravity on objects.

4. How does 't Hooft's introduction to general relativity differ from other textbooks on the subject?

't Hooft's introduction to general relativity is known for its clear and intuitive explanations of complex concepts. It also places a strong emphasis on the Rindler transformation and its applications, which is not always covered in other textbooks. Additionally, it includes exercises and problems that help readers deepen their understanding of the material.

5. Is 't Hooft's introduction to general relativity suitable for beginners?

't Hooft's introduction to general relativity is written for readers with a basic understanding of mathematics and physics. While it may be challenging for complete beginners, it is a great resource for those looking to deepen their understanding of general relativity and the Rindler transformation.

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