Question

Since the magnetic field is simply an interpretation of the effects of length contraction on charges and the electric field (see en.wikipedia.org/wiki/Relativistic_electromagnetism), could one formulate (or have people already formulated) an analog to the gravitational field that functions like the magnetic field. Since the gravitational and electric fields behave so similarly, I figure, at least mathematically, it would be possible to account for the length contraction of objects in the gravitational effects by pairing the gravitational field with another one.

Answer 1

For instance, let the analog of the magnetic field be \(\vec Y\), which would then allow us to construct analogs for Maxwell's equations (here \(\rho\) is mass density).\[\vec \nabla \cdot \vec g = 4\pi G \rho\]\[\vec \nabla \cdot \vec Y = 0\]\[\vec \nabla \times \vec g = \cdots \]\[\vec \nabla \times \vec Y = \cdots \]Could I even go so far as to say that since we know gravitational waves travel at the speed of light, that the analog of \(\mu_0\) could be calculated through the constant \(4\pi G\) thruogh an analog of \(c = \dfrac{1}{\sqrt{\mu_0 \epsilon_0}}\)? These are all just things I'm just thinking about off the top of my head... any feedback?

Answer 2

I'm sorry, I have nothing to say but I want to track this question because this is a really interesting notion.. so I'm leaving this reply to make sure I follow the answers. I'll be searching for an answer myself as well, maybe I can find something.

Answer 3

Just one correction: (forgot a minus sign) \(\vec \nabla \cdot \vec g = - 4\pi G \rho\)

Answer 4

don't have any idea about it, did u check general relativity for an answer?