Understanding the Minkowski Metric: Explained Step-by-Step for Beginners

In summary, the metric tensor is a coordinate-independent quantity that assigns an inner product to each fiber of the tangent bundle of space-time. It can be expressed in different coordinate systems, but the value it gives remains the same regardless. Other types of metrics, such as the Schwarzschild metric, are used in General Relativity to describe different space-time geometries and are not related to measuring distances in different coordinate systems. The x, y, z, t (4 dimensions) are measured in the Lorentzian metric, and the Schwarzschild metric is used to measure around spherically symmetric bodies like planets and black holes. The Lorentzian metric can take a general form in General Relativity, and is not necessarily related
  • #36
LastOneStanding said:
More importantly, it makes it possible to start understanding the physics as quickly as possible.
To conclude, I think this is the whole crux of it all. If the goal is to learn the physics then yeah go right into the relevant physics text but there will be people, me included, who are just uncomfortable in learning physical theories at the level of GR or QM etc. without some exposition to the math as presented in a math text, beforehand.

However I think GR is funny in the sense that even if you do learn differential geometry from a math text beforehand, you will still not be able to do any of the problems involving tensor calculus (like the one I posted a solution to in post #7 of this thread) until you actually pick up a GR book and start reading it because as far as I've seen, no modern differential geometry text even touches the index based tensor calculations that you see so pervasively in e.g. Wald.
 
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  • #37
Hello,

Thank you for referring the source. I would start shortly with Hartle's Gravity. Honestly speaking, I am a self-learner. There are some concepts which are not clear in my mind. Hence, when I ask questions, naive, it might seemed idiotic. So, I refrain. Definitely I would go ahead with the references. Differential geometry would take some time, I believe. Anyway...

Thanks for all the help.
 

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