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This question already has an answer here:

Which book can i refer to gain a great deal of aspects on Schwarzchild metric without any tensor calculus

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marked as duplicate by Qmechanic Feb 15 '17 at 7:02

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  • $\begingroup$ Wikipedia, or any introductionary level book about the General Relativity. Without tensors, it doesn't work, because the GR is based on them. If you have a more specific question about the Schw.-metric, I suggest to ask this here. Asking for a book name is unfortunately not allowed here as an ordinary question (maybe others will explain its reason), but after you've made some good question or answer, you will be able to take part in the chatroom of the site, where you can ask this. $\endgroup$ – peterh Feb 15 '17 at 7:03
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Take a look at the book "Differential Forms and the Geometry of General Relativity" by Tevian Dray (Professor Mathematics at Oregon State University). Published by CRC Press.

Professor Dray is motivated to teach General Relativity from the perspective of Differential Forms instead of coordinate based notation using Tensors. This book is divided into three parts. Parts I & II cover General Relativity from a vector Calculus approach describing the geometry of spacetime and curvature. Part III is almost a separate "course" on Differential Forms but actually some aspects of Differential Forms are introduced earlier in the text as well (Chapt. 6 is called "Warmup" and covers differential forms in a nutshell as well as Hodge Dual, Exterior Derivatives, Connections, and Curvature).

Here is the Amazon link where you can read more about the book and see the table of contents: Differential Forms And The Geometry Of General Relativity

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