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So I have taken a math course dealing with the mathematics behind GR. In it I learnd how to calculate many of the objects that GR deals with such as curvature tensors, geodesics and so on. However, not much physical explination into how these object tie into gravity was discussed (due to time constraints) and the emphasis was in calculation rather than the theory behind.

So now i am trying to tie in the theory with what i can calculate using a metric.

I was wondering if i could get an explination on how to relate these curvature tenors back to physical space. For example, say I wanted to create a program that plots the amount of curvature around a spherical body using a colour scheme (darker = more curvature) what would I use to do this as far as the "tools" avaliable such as the tensors in the Einstein Tensor?

thanks