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This book continues our exploration of the most profound theory of science, Einstein’s General Theory of Relativity. All of modern astrophysics and cosmology stands on the foundation of General Relativity that is best expressed in tensors.This book, and its sequel, General Relativity 4: Astrophysics & Cosmology, present the clearest, most comprehensible, and most complete introduction to the tensor calculus of differential topology, which Einstein used to explain the cosmos. Derivations that are difficult to find elsewhere, are all collected here and explained in detail.This book presents all the principle tensors of General Relativity, and explains how these are computed and utilized. We apply our new expertise to:- the derivation of the Schwarzchild metric- the bending of starlight- stable and unstable orbits around black holes- the mass-energy tensor- the precession of Mercury and binary pulsars.Those who love mathematical challenges need look no further. Others can bypass the appendices, which contain the most advanced material.

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