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.

 

[sardar]

The use of Riemann tensor calculus in modelling space-time is a powerful tool in the study of general relativity. It allows us to describe the curvature of space-time and how it is affected by the presence of matter and energy.

Through Riemann calculus, we are able to mathematically represent the four-dimensional fabric of space-time and understand how it is warped by the presence of massive objects. This allows us to explain phenomena such as gravitational lensing, where the path of light is bent by the curvature of space-time around massive objects.

Riemann calculus also plays a crucial role in predicting the behavior of celestial bodies, such as the orbit of planets around the sun. By understanding the curvature of space-time, we are able to accurately calculate the trajectories of these objects.

In summary, the use of Riemann tensor calculus in modelling space-time provides us with a deeper understanding of the fundamental principles of the universe and allows us to make precise predictions about the behavior of objects in space.