# EM Tensor and GR

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

## Answers and Replies

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.

WannabeNewton
Science Advisor
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.

dextercioby
Science Advisor
Homework Helper
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).