Problems with the Riemann tensor in general relativity

Click For Summary
SUMMARY

The discussion centers on the derivation of the Riemann tensor in general relativity, specifically addressing the validity of equation (3) and its relation to the second order derivative. The user successfully derived equation (1) using Taylor expansion and equations (2) but seeks clarification on how to proceed from equation (4) to express the second order derivative. The user also questions the correctness of equation (3) and requests guidance on continuing the derivation if it is incorrect.

PREREQUISITES
  • Understanding of Taylor expansion in the context of differential geometry
  • Familiarity with the Riemann tensor and its properties in general relativity
  • Knowledge of second order derivatives and their applications in tensor calculus
  • Ability to interpret and manipulate mathematical equations in theoretical physics
NEXT STEPS
  • Review the derivation of the Riemann tensor from the metric tensor in general relativity
  • Study the implications of equation (3.71) in the context of curvature and derivatives
  • Explore the relationship between the Riemann tensor and the second order derivatives in tensor calculus
  • Investigate common pitfalls in deriving equations related to the Riemann tensor
USEFUL FOR

Students and researchers in theoretical physics, particularly those focusing on general relativity and differential geometry, will benefit from this discussion.

Ineedhelpimbadatphys
Messages
9
Reaction score
2
Homework Statement
In the picture.
Relevant Equations
Also in pictures.
IMG_2750.jpeg
IMG_2752.jpeg

After Taylor expansion and using equations (2), I have no problem getting to equation (1). Now obviously I have to somehow use (3.71) ,which I do know how, to derive to express the second order derivative.
On the internet I found equation (3), and I have tried to understand where this comes from (4).
Is equation (3) correct, if yes, how am i supposed to contineu from what I have in (4). It should equal 3 times the secobd order derivative?

If equation (3) is not correct, any tips how to continue from what I have?
 
Physics news on Phys.org
The sentence after (3.71) was a little unclear. I meant that I do know how to derive (3.71) using equations (2).
 

Similar threads

Variation of quadratic Riemann Curvature tensor
  • · Replies 7 ·
Replies
7
Views
2K
Riemann curvature coefficients using Cartan structure equation
  • · Replies 2 ·
Replies
2
Views
2K
General relativity - Using Ricc and Weyl tensor to find the area
  • · Replies 1 ·
Replies
1
Views
2K
Proving the symmetry property of Riemann curvature tensor
  • · Replies 1 ·
Replies
1
Views
5K
Riemann tensor given the space/metric
  • · Replies 7 ·
Replies
7
Views
3K
Specific proof of the Riemann tensor for FRW metric
  • · Replies 2 ·
Replies
2
Views
3K
Calculating the components of the Ricci tensor
  • · Replies 6 ·
Replies
6
Views
3K
How Do You Calculate the Ricci Tensor for the AdS Metric in 4 Dimensions?
  • · Replies 1 ·
Replies
1
Views
4K
Solving a Problem with Interchanging Field Tensors
  • · Replies 5 ·
Replies
5
Views
2K
Graduate GW Binary Merger: Riemann Tensor in Source & TT-Gauge
  • · Replies 4 ·
Replies
4
Views
2K