The modelling of space time through Riemann tensor calculus

[aditya ver.2.0]

How do we explains space-time through Riemann Calculus?

 

[pervect]

Riemann calculus is really needed only to describe curvature, not space-time.

The mathematical structure of space-time, like the mathematical structure of just space, is that of a manifold. A manifold is built on top of some other math concepts, I'm not sure if I should go into that level of detail, for the moment I won't.

We had another thread recently on why we combine space and time into a unified "space-time". This basically comes not from mathematics, but rather from special relativity.

 

[Vanadium 50]

You might want to read this: https://www.physicsforums.com/threads/very-little-excuse-to-ask-a-question-cold.765735/

Essentially, your question is "please write a textbook on GR for me here". That's too much to ask, and doing so disrespectful of other people's time. You need to start doing some work on your own.

 

[Nugatory]

What Vanadium50 said. This thread is closed, but more specific and focused questions in new threads will be welcome.