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How does the knowledge of tensor analysis and Differential Geometry help us understand the equations of General and Special Relativity?

Qmechanic
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Achyuth SS
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    If you want a shallow understanding of GR only, just knowing calculus and being acclimated with tensor indices suffices. But if you want a deeper understanding, you have to go through the tensor analysis and differential geometry, mainly because it is pretty much all GR is about. – Jeanbaptiste Roux Sep 08 '22 at 07:46
  • Could you add more detail on your background? This seems like a weird question to ask if you've already worked with GR, so to give a proper answer it would be useful to know what can be assumed. – Níckolas Alves Sep 08 '22 at 07:50
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    Related: Why do we need tensors in modern physics? – Níckolas Alves Sep 08 '22 at 07:52
  • Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. – Community Sep 08 '22 at 08:08
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    Vector and tensor calculus and analysis should be prerequisites for any approach to any branch of Physics, not only SR or GR, since tensors are the mathematical tools that describes the absolute nature of physics, i.e. its independence from the coordinates you use to describe it. If you understand what you're doing using tensors, and not only their components, all the strange concepts like covariant differentiation, are not so strange anymore – basics Sep 08 '22 at 08:11
  • How can you understand the Einstein field equations $R_{\mu\nu}-\frac12Rg_{\mu\nu}+\Lambda g_{\mu\nu}=\frac{8\pi G}{c^4}T_{\mu\nu}$ without understanding tensors? – Ghoster Sep 08 '22 at 20:57

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