Plot of the Fabric of Spacetime - Schwarzschild

[fobos3]

Hi there. I am trying to plot the fabric of spacetime caused by an object using the schwarzchild solution. The idea is to replace one of the basis of space with time. I have computed $$R_{\mu\nu}$$, $$R$$ and $$T_{\mu\nu}$$ but I'm stuck here. How do I get to the equation of the surface from here? Any help will be appreciated.

 

[A.T.]

What surface do you want to plot? This is about curved 2d-spacetime embedded in 3d:
http://www.relativitet.se/Webarticles/2001GRG-Jonsson33p1207.pdf

 

[Entropia]

The Schwarzschild solution is a mathematical model that describes the fabric of spacetime around a spherically symmetric object, such as a black hole. It is based on the theory of general relativity, which explains how gravity affects the curvature of spacetime.

To plot the fabric of spacetime using the Schwarzschild solution, you will need to use the Ricci tensor (R_{\mu\nu}), the Ricci scalar (R), and the stress-energy tensor (T_{\mu\nu}). These quantities represent the curvature of spacetime and the distribution of matter and energy within it.

Once you have calculated these values, you can use them to construct the equation of the surface of the fabric of spacetime. This equation will give you a visual representation of how the curvature of spacetime changes near the object.

To get to this equation, you will need to use the Einstein field equations, which relate the Ricci tensor and scalar to the stress-energy tensor. These equations can be solved for the metric tensor, which describes the geometry of spacetime.

I would recommend consulting a textbook or seeking guidance from a professor or tutor to help you navigate this process. It can be complex and may require a strong understanding of differential geometry and general relativity. Good luck with your project!