Understanding the Role of Tensor Calculus in General Relativity

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In an attempt to solve the mystery of dark energy, I came across problems concerned with the General Relativity. In it, I observed that many of the problems were related with the tensor calculus.
I want to know that what importance does tensor calculus hold in GR? Are there any other fields of mathematical that too play an important role in the subject?
 
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Your intentions are bold, for sure. You cannot conceive General Relativity in the absence of tensor calculus. Usually tensor calculus is seen as a part of differential geometry, so any mathematical prerequisites of diffgeo are mandatory: multivariable real calculus, linear algebra and a little point set topology + solving ODEs (to which the non-linear PDEs of GR can be usually reduced).
 
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General relativity is expressed in tensor calculus. You can't have GR without it.

I guess the analogy would be "what importance does English have to Shakespeare's plays?"
 

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