Gravity - Fluid Dynamics in Curved Time-space

[physicsismylife]

Let's begin this thread with an excercise. If you think, that you're good at calculating things, I have an interesting problem to solve. I would like you, to use the basic rules of General Relativity - Einstein's field equations, combined with interior and exterior Schwarzschild solutions - to describe the gravitational field as an embedding diagram. Here is the basic knowledge, regarding the given problem:

https://en.wikipedia.org/wiki/Introduction_to_general_relativity#From_acceleration_to_geometry

https://en.wikipedia.org/wiki/Interior_Schwarzschild_metric

Here is an example, how to make such diagram for the Sun and Earth:
http://www.johnstonsarchive.net/relativity/stcurve.pdf
Try to use this knowledge, to define the gravitational field of an empty spherical shell with mass M (interior and exterior fields) - and compare the results with Newton's theorem...

Next step will be to change the interior of spherical shell and turn it into uniform distribution of matter - which can be treated as a liquid medium.
Now, you should include those two properties of liquids:

Hydrostatic pressure:
https://en.wikipedia.org/wiki/Hydrostatics

Surface tension:
https://en.wikipedia.org/wiki/Surface_tension

If you are rally good at calculating things, you should end up with a solution, which should be capable to properly explain those two scenarios:

If you will succeed, I will give you 40% of credit - so it's possible, that you can be quite famous

But in the meantime, I will keep explaining the subject of gravity and fluid dynamics, in my own way. My goal is to see, if the calculations will match my predictions...

3... 2... 1... Go!
Good luck!

[Endy0816]

Gravity is common to both, but virtual shape of the 3D black hole is different than that representation. More of a bubble or void.

 

Keep in mind this is a place for 2-way discussion. Science is about sharing knowledge and generally whoever does the work of proving an idea gets the credit.