EM Tensor & GR: Does Space Curvature Impact EM Field?

  • Context: Graduate 
  • Thread starter Thread starter kroni
  • Start date Start date
  • Tags Tags
    Em Gr Tensor
Click For Summary

Discussion Overview

The discussion revolves around the relationship between electromagnetic (EM) fields and spacetime curvature in the context of General Relativity (GR) and Yang-Mills theory. Participants explore whether variations in space curvature can create or modify EM fields, examining theoretical implications and equations involved.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Clément questions whether space curvature impacts the EM field and if variations in curvature can create an EM field.
  • One participant asserts that the gravitational field is created by the energy density of the EM field, suggesting that the relationship is not reciprocal.
  • Another participant references Yang-Mills theory, proposing that changes in the curvature of the base manifold could modify the connection in the fiber bundle, potentially affecting the EM field.
  • A later reply agrees that spacetime curvature affects EM fields but emphasizes that a source of charges is necessary to generate the EM field initially.
  • Another participant elaborates that the existence of spacetime curvature modifies the field equations, indicating that they become more complex than the standard Maxwell equations.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the relationship between spacetime curvature and EM fields. While some acknowledge that curvature affects EM fields, others maintain that curvature alone does not create EM fields without the presence of charges. The discussion remains unresolved regarding the extent and nature of this interaction.

Contextual Notes

Participants reference specific theories and equations, such as the Einstein-Maxwell equations and Yang-Mills theory, but do not resolve the implications of these theories on the relationship between curvature and EM fields. The discussion includes assumptions about the definitions and roles of curvature and EM fields that are not explicitly clarified.

kroni
Messages
79
Reaction score
10
Hello,

I am reading a book about General relativity, i understand that energy of the EM tensor go in the stress- energy tensor of GR equations. SO, EM field curve space. But i don't understand if space curvature impact EM field ? Is variation of space curvature can create EM field ?

Clément
 
Physics news on Phys.org
kroni said:
Hello,

I am reading a book about General relativity, i understand that energy of the EM tensor go in the stress- energy tensor of GR equations. SO, EM field curve space. But i don't understand if space curvature impact EM field ? Is variation of space curvature can create EM field\?
No. The gravitational field is created by virtue of the EM field's energy density which has mass density. It's not the other way around though. I.e. just because something has something has mass density it doesn't mean that it has an EM field.
 
If i make no mistake, In yang mills theory, EM tensor is define as the connection in a fiber bundle with S1 Lie group, it seems logic to me that if base manifold has a changing curvature, the connection in the fiber bundle may change. So, space curvature might modify EM field. I will try to put this in equation to see where is my problem.
 
Yes spacetime curvature affects the EM fields present but that doesn't change what Mike said. You need a source of charges to generate the EM field in the first place for spacetime curvature to affect. See Einstein-Maxwell equations.
 
kroni said:
If i make no mistake, In yang mills theory, EM tensor is define as the connection in a fiber bundle with S1 Lie group, it seems logic to me that if base manifold has a changing curvature, the connection in the fiber bundle may change. So, space curvature might modify EM field. I will try to put this in equation to see where is my problem.

Yes, you are correct, the existence of space(time) curvature modifies the way the field looks like, simply because the PDE's for the field equations get extra terms, they are no longer the linear nicely-looking Maxwell Equations anymore. In the Y-M, we call them gauge potential (connection) and gauge field (curvature of the connection).
 

Similar threads

  • · Replies 27 ·
Replies
27
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 51 ·
2
Replies
51
Views
5K
  • · Replies 38 ·
2
Replies
38
Views
3K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 18 ·
Replies
18
Views
1K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 26 ·
Replies
26
Views
3K
  • · Replies 21 ·
Replies
21
Views
525