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.pdfTry 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!