A College Course on Relativity and Cosmology

Abstract

Abstract This book introduces Einstein’s general theory of relativity. Topics include the geometric formulation of special relativity, the principle of equivalence, the Einstein field equation and its spherical solution, and black holes, as well as cosmology. The subject is presented with an emphasis on physical examples and simple applications without the full tensor apparatus (although, for those wishing to have a glimpse at the proper tensor formulation of Einstein’s field equation, this is presented in a final chapter). The reader first learns the physics of the equivalence principle and how it inspired Einstein’s idea of curved spacetime as the gravitational field. At the mathematically more accessible level of a metric description of a warped space, the reader can already study many interesting phenomena, such as gravitational time dilation, GPS operation, light deflection, precession of Mercury’s perihelion, and black holes. Many modern topics in cosmology are discussed: from primordial inflation and the cosmic microwave background, to the dark energy that propels an accelerating universe.