Proving Non-Absorbable Constant with Δξgμν

  • Thread starter Morgoth
  • Start date
  • Tags
    Constant
In summary, in this conversation, the speaker is discussing a problem involving the metric of a sphere given as ds2= α (dθ2+ sin2θ dφ2) and being asked to prove that the constant α is non-absorbable. They are asked to show that there is no solution to the set of equations Δξgμν = ∂gμν/∂α, and to provide another way to prove this. They mention having trouble understanding the concept of non-absorbable and ask for any hints or resources to help solve the problem. The equations they have arrived at cannot be solved and they also mention a problem with 0=1.
  • #1
Morgoth
126
0
Well I have the metric of a sphere given as:
ds2= α (dθ2+ sin2θ dφ2 )

And I'm asked to prove that the constant α is non-absorbable by proving there is no solution to this set of equations:
Δξgμν = ∂gμν/∂α

where:
Δξgμν = gμν;λ ξλ + gλν ξλ;μ + gμλ ξλ;ν


Finally, I'm asked to provide a second way to prove that α is non-absorbable.



I don't understand what it means by non-absorbable at all. Do you know where am I supposed to find what it is? From books I have Weinberg's "Gravitation and Cosmology Principles and appls of GTR". In addition, any hint would be appreciated...
Thank you..
 
Physics news on Phys.org
  • #2
28c3d3m.jpg


This is my 1st try to solve it, the equations I ended up are the 5 bellow, which cannot be solved (i guess). The last one reads ξ2,2=1/2α..

I also got a problem with 0=1...

What do you think?
 

1. What is "Proving Non-Absorbable Constant with Δξgμν"?

"Proving Non-Absorbable Constant with Δξgμν" is a scientific process that involves using mathematical equations to demonstrate that a particular constant, Δξgμν, is non-absorbable. This means that the value of Δξgμν remains constant throughout an experiment or observation, regardless of any external factors.

2. Why is it important to prove that Δξgμν is non-absorbable?

Proving that Δξgμν is non-absorbable is important because it allows for more accurate and reliable results in scientific experiments and observations. It also helps to validate the mathematical models and theories used in various scientific fields.

3. How is "Proving Non-Absorbable Constant with Δξgμν" different from other scientific processes?

"Proving Non-Absorbable Constant with Δξgμν" is a specific process that focuses on demonstrating the non-absorbability of a constant. Other scientific processes may involve proving the existence of a constant or determining its value, but not necessarily its non-absorbability.

4. What are the steps involved in "Proving Non-Absorbable Constant with Δξgμν"?

The steps involved in "Proving Non-Absorbable Constant with Δξgμν" typically include identifying the constant, setting up a mathematical model or equation, conducting experiments or observations, analyzing data, and drawing conclusions based on the results.

5. How is the non-absorbability of Δξgμν determined?

The non-absorbability of Δξgμν is typically determined by comparing the values of the constant before and after an experiment or observation. If the value remains constant, regardless of any external factors, then it can be concluded that Δξgμν is non-absorbable.

Similar threads

A Electromagnetic tensor and time reversal
    • Special and General Relativity
Replies
6
Views
2K
Colinear points in a vectorplane
    • Precalculus Mathematics Homework Help
Replies
4
Views
3K
A Prove Constant Curvature: Homogeneity Implied by Cosmological Principle
    • Special and General Relativity
Replies
8
Views
1K
Questions about Properties of the Godel Metric
    • Special and General Relativity
Replies
6
Views
1K
Relationship Between Spatial Expansion and Gravity's Force?
    • Special and General Relativity
Replies
13
Views
2K
I An exception to the principle of equivalence?
    • Special and General Relativity
Replies
18
Views
2K
I I Came Up with a CTC in Minkowski Space: Exploring To What End?
    • Special and General Relativity
Replies
7
Views
1K
Null curve coordinate system
    • Calculus and Beyond Homework Help
Replies
5
Views
1K
A Gravitational field of an infinite flat slab
    • Special and General Relativity
Replies
14
Views
3K
Transformation to locally flat coordinates
    • Special and General Relativity
Replies
20
Views
4K

Hot Threads

Recent Insights

Back
Top