Relativity, Gravitation and Cosmology: A Basic Introduction
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 an 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.
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accelerating accelerating universe angular baryon basis vectors big bang black hole calculate Chapter Christoffel symbols clock components coordinate system coordinate transformations cosmic cosmological constant covariant curvature tensor curved space curved spacetime dark matter deﬁned deﬁnition discussed distance Einstein equation electromagnetic elements energy density energy–momentum epoch Euclidean expansion ﬁnd ﬁrst ﬁxed ﬂat space ﬂat universe ﬂuid ﬂux Friedmann equations galaxies geodesic equation geometry gravitational ﬁeld gravitational potential gravitational time dilation gravitational wave Hubble inertial frames inﬂation inﬂationary interval invariant light Lorentz transformation luminosity mass density matrix Maxwell’s metric function metric tensor neutrinos Newton’s Newtonian nonrelativistic observer orbit parallel transport parameter particle photon Problem quantum radiation redshift reﬂects relation relativistic relativity result rotation scalar scale factor Schwarzschild Section solution spatial spherical star surface symmetry temperature theory vacuum velocity worldline µν