2
votes
1answer
215 views

How to properly construct the electromagnetic tensor in curved space-time?

How do I properly construct the electromagnetic tensor in curved space-time? I have my curved spacetime metric $(+,-,-,-)$ and my magnetic vector potential $A$. I tried two ways but not sure which is ...
1
vote
1answer
46 views

Homogeneity and isotropy of stress energy tensor

Given the energy momentum tensor in E&M: $T_{\mu\nu} = -F_{\mu\alpha} g^{\alpha \beta} F_{\beta \nu} +\frac{1}{4} g_{\mu \nu} F_{\sigma \alpha} g^{\alpha \beta} F_{\beta \rho} g^{\rho \sigma}$ I ...
1
vote
1answer
74 views

Has a metric formulation of electromagnetism ever been attempted? [duplicate]

I understand that electromagnetic fields carry energy, and this energy curves spacetime gravitationally. That's not my question. I'm asking if anyone has tried to formulate electromagnetism in such ...
3
votes
1answer
115 views

Solving electromagnetic vector field using the Lagrangian

Given an action of the form \begin{equation}S=-\frac{1}{4}\int d^4x\eta^{\mu\nu}\eta^{\lambda\rho}F_{\mu\lambda}F_{\nu\rho}\end{equation} where ...
3
votes
2answers
273 views

The signature of the metric and the definition of the electromagnetic tensor

I've read the definition of the electromagnetic field tensor to be ...
9
votes
2answers
443 views

Does Kaluza-Klein Theory Require an Additional Scalar Field?

I've seen the Kaluza-Klein metric presented in two different ways., cf. Refs. 1 and 2. In one, there is a constant as well as an additional scalar field introduced: $$\tilde{g}_{AB}=\begin{pmatrix} ...