Does Gravitational Field Flux Cause Gravitational Waves?

[Saksham Dhull]

As most of know that magnetic field arises due to change in electric field flux over a surface.
In the same way, is there any kind of field arising due to gravitational field flux about a surface ?
And if yes then does gravitational field and that field cause each other (in the same way electric field and magnetic fields do)?

 

[Drakkith]

In the same way, is there any kind of field arising due to gravitational field flux about a surface ?

I believe there are some analogous effects, but not exactly. Have a look at this wiki article*: https://en.wikipedia.org/wiki/Gravitoelectromagnetism
As the article states in the first paragraph, these are analogies and approximations that are only valid in certain situations. There is still only one gravitational field, just like there is only one electromagnetic field (the electric and magnetic components are joined into a single field). I've never heard of the gravitational field being split into multiple components, so I assume the analogies and approximations are not that useful in most cases where we do calculations involving gravity.

*This article's reliability is questionable, as it is lacking valid references in many areas.

 

[Khashishi]

The gravitational field is described by the Riemann curvature tensor, which has 20 components. (In contrast, the electromagnetic field has 6 independent components.) You can break down the Riemann curvature tensor into smaller parts. See https://en.wikipedia.org/wiki/Ricci_decomposition
One of the parts is the Weyl curvature. There are gravitational waves which are oscillations in the Weyl curvature.