Schwarzschild Metric - Rindler coordinates

In summary, the Schwarzschild metric is a mathematical formula used to describe the curvature of space-time around a non-rotating, spherically symmetric object, such as a black hole. Rindler coordinates are a set of coordinates related to the Schwarzschild metric that are used to describe the space-time around an accelerating object. The Schwarzschild radius, also defined by the metric, represents the point at which the gravitational pull of a black hole becomes so strong that not even light can escape. The metric is commonly used in astrophysics to study the properties of black holes and other massive objects in the universe.
  • #1
aCHCa
4
0
Hello, well I just read a paper by Atish Dabholkar and Ashoke Sen, titled "Quantum Black Holes", pp. 4-5 as shown below

1PF.jpg


2pf-1.jpg


and I tried to find [itex]d\xi^{2}\frac{2GM}{\xi}=d\rho^{2}[/itex] like this

3pf-1.jpg


which is different from the eq. in the paper.

So, could somebody please help me to find my mistake in the calculation? Thank you
 
Physics news on Phys.org
  • #2
ρ2 = 8GM ξ
ρ = √8GM √ξ
dρ = √8GM ½dξ/√ξ = √2GM dξ/√ξ
2 = 2GM dξ2
 
  • #3
Ah thank you so much :D
 

1. What is the Schwarzschild Metric?

The Schwarzschild metric is a mathematical formula used in general relativity to describe the curvature of space-time around a non-rotating, spherically symmetric object, such as a black hole. It was first derived by German physicist Karl Schwarzschild in 1916.

2. What are Rindler coordinates?

Rindler coordinates are a set of coordinates used to describe the space-time around an accelerating object. They are often used in the study of black holes and are related to the more commonly used Schwarzschild coordinates.

3. How are Rindler coordinates related to the Schwarzschild metric?

Rindler coordinates are a special case of the Schwarzschild metric in which the observer is accelerating. In this case, the Schwarzschild metric can be transformed into Rindler coordinates, which provide a more convenient way to describe the space-time around an accelerating object.

4. What is the significance of the Schwarzschild radius in the Schwarzschild metric?

The Schwarzschild radius is a characteristic distance defined by the Schwarzschild metric that represents the point at which the gravitational pull of a black hole becomes so strong that even light cannot escape from it. It is also known as the event horizon of a black hole.

5. How is the Schwarzschild metric used in astrophysics?

The Schwarzschild metric is used in astrophysics to study the properties of black holes and other massive objects in the universe. It allows scientists to make predictions about the behavior of objects in the vicinity of a black hole and to understand how gravity affects the curvature of space-time.

Similar threads

  • Special and General Relativity
Replies
9
Views
964
Replies
13
Views
475
Replies
1
Views
921
  • Special and General Relativity
Replies
19
Views
1K
Replies
2
Views
815
  • Special and General Relativity
Replies
18
Views
1K
  • Special and General Relativity
2
Replies
43
Views
2K
  • Special and General Relativity
2
Replies
35
Views
3K
  • Special and General Relativity
Replies
8
Views
1K
  • Special and General Relativity
Replies
3
Views
2K
Back
Top