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You just call it something like T. If you want any numbers you need a coordinate basis.

For those interested, the first chapter of Kip Thorne's book has a good, though idiosyncratic, explanation of tensors: http://www.pmaweb.caltech.edu/Courses/ph136/yr2012/1201.1.K....



The first lectures here https://theoreticalminimum.com/courses/general-relativity/20... are mostly an introduction to tensor calculus.




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