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