Einstein's general theory of relativity is introduced in this advanced undergraduate and beginning graduate level textbook.  Topics include special relativity in the formalism of Minkowski's four-dimensional space-time, the principle of equivalence, Riemannian geometry and tensor analysis, Einstein's field equation and cosmology. The author presents the subject from the very beginning with an emphasis on physical examples and simple applications without the full tensor apparatus.  One first learns how to describe curved spacetime.  At this mathematically more accessible level, the reader can already study the many interesting phenomena such as gravitational lensing, precession of Mercury's perihelion, black holes, as well as cosmology. The full tensor formulation is presented later, when the Einstein equation is solved for a few symmetric cases. Many modern topics in cosmology are discussed in this book: from inflation and cosmic microwave anisotropy to the "dark energy" that propels as accelerating universe. Mathematical accessibility, together with the various pedagogical devices (e.g., worked-out solutions of chapter-end problems), make it practical for interested readers to use the book to study general relativity, gravitation and cosmology on their own.

Relativity, gravitation, and cosmology: a basic introduction PDF

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