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This reference textbook is an up-to-date and self-contained introduction to the theory of gravitational interactions. The first part of the book follows the traditional presentation of general relativity as a geometric theory of the macroscopic gravitational field. A second, advanced part then discusses the deep analogies (and differences) between a geometric theory of gravity and the gauge theories of the other fundamental interactions. This fills a gap which is present in the context of the traditional approach to general relativity, and which usually makes students puzzled about the role of gravity. The necessary notions of differential geometry are reduced to the minimum, leaving more room for those aspects of gravitational physics of current phenomenological and theoretical interest, such as the properties of gravitational waves, the gravitational interactions of spinors, and the supersymmetric generalization of the Einstein equations.
Theory of Gravitational Interactions will be of particular value to undergraduate students pursuing a theoretical or astroparticle curriculum. It can also be used by those teaching related subjects, by PhD students and young researchers working in different scientific sectors but wishing to enlarge their spectrum of interests, and, in general, by all scholars interested in the modern aspects and problems of gravitational interaction.

Theory of Gravitational Interactions

Elementary notions of relativistic field theory.- Towards a relativistic theory of gravity.- Tensor calculus in a Riemannian manifold.- Maxwell equations and Riemann geometry.- Test bodies and signals in a Riemann spacetime.- Geodesic deviation and curvature tensor.- The Einstein equations for the gravitational field.- The weak field approximation.- Gravitational waves.- The Schwarzschild solution.- The Kasner solution.- Vierbeins and Lorentz connection.- The Dirac equation in a gravitational field.- Supersimmetry and supergravity.- Appendix A. The language of differential forms.- Appendix B. Higher-dimensional gravity.