Move Stress-Energy tensor to the left side of EFE?

  • Context: Undergrad 
  • Thread starter Thread starter Fractal matter
  • Start date Start date
  • Tags Tags
    Energy Stress Tensor
Click For Summary
SUMMARY

The discussion centers on the placement of the Stress-Energy tensor (SET) in the Einstein Field Equations (EFE). Participants assert that moving the SET to the left side of the EFE, resulting in the equation R - T = 0, does not alter the physical implications of the equation. The consensus is that regardless of whether the SET is on the left or right side, it does not create a vacuum, as a vacuum is defined by the SET being zero. The mathematical equivalence of the configurations is emphasized, highlighting that the placement of tensors does not change the underlying physics.

PREREQUISITES
  • Understanding of Einstein Field Equations (EFE)
  • Familiarity with Stress-Energy Tensor (SET)
  • Knowledge of cosmological constant (Λ) and its implications
  • Basic principles of general relativity
NEXT STEPS
  • Explore the implications of moving tensors in general relativity
  • Study the role of the cosmological constant in EFE
  • Investigate the definition and properties of vacuum in general relativity
  • Learn about the mathematical equivalence of tensor equations in physics
USEFUL FOR

Physicists, students of general relativity, and anyone interested in the mathematical foundations of gravitational theories.

Fractal matter
Messages
34
Reaction score
14
Is it possible to move Stress-Energy tensor to the left side of EFE? R=T => R-T=0. Relativists move cosmological constant Λ to the right side of EFE. Can we move SE tensor to make a vacuum?
 
Physics news on Phys.org
You can move either tensor to either side. It makes no difference to anything. Because we don't know what dark energy/the cosmological constant is you can argue that it's a part of spacetime or it's a part of the contents of spacetime, and then it kind of makes sense to put it with the Einstein tensor or with the stress-energy tensor just in a birds-of-a-feather kind of way. The maths is the same, whichever side you put it.

You can take the stress-energy tensor to the same side as the Einstein tensor if you like. It doesn't make matter into a vacuum (unless it was already a Hoover).

"Two apples equals two apples" is equivalent to "two apples minus two apples is no apples". Neither statement makes any difference to the contents of my fruit bowl.
 
Reply
  • Like
Likes   Reactions: ohwilleke and Orodruin
Fractal matter said:
Can we move SE tensor to make a vacuum?
No. "Vacuum" is defined as the SET being zero. Which side of the equation you put the SET on is irrelevant to that.
 

Similar threads

Undergrad Cauchy Stress Tensor in Applied Strength of Materials
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Obtaining the matter Lagrangian from the stress energy tensor
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Can We Explain the Cosmological Constant as a Tensorial Concept?
  • · Replies 12 ·
Replies
12
Views
2K
Graduate Going from Cauchy Stress Tensor to GR's Energy Momentum Tensor
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Piecewise Functions in the Einstein Field Equations
  • · Replies 57 ·
2
Replies
57
Views
4K
Undergrad Equation of state for Einstein field equations
  • · Replies 4 ·
Replies
4
Views
1K
Undergrad Adapting Schwarzschild Metric for Nonzero Λ
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Dirac's integral for the energy-momentum of the gravitational field
  • · Replies 38 ·
2
Replies
38
Views
1K
Undergrad Understanding the Stress-Energy Tensor in Special Relativity
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Dirac on localization of energy in the gravitational field
  • · Replies 16 ·
Replies
16
Views
2K