Vittorio N. An Overview of General Relativity and Space-Time 2023

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Vittorio N. An Overview of General Relativity and Space-Time 2023

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Textbook in PDF format This textbook equips Masters’ students studying Physics and Astronomy with the necessary mathematical tools to understand the basics of General Relativity and its applications. It begins by reviewing classical mechanics with a more geometrically oriented language, continues with Special Relativity and, then onto a discussion on the pseudo-Riemannian space-times. Applications span from the inner and outer Schwarzschild solutions to gravitational wave, black holes, spherical relativistic hydrodynamics, and Cosmology. The goal is to limit the abstract formalization of the problems, to favor a hands-on approach with a number of exercises, without renouncing to a pedagogical derivation of the main mathematical tools and findings. Part I From Forces to Curvature Space and Time: The Classical View From Space and Time to Space-Time From Inertial to Non-Inertial Reference Frames Pseudo-Riemannian Spaces The Riemann-Christoffel Curvature Tensor From Non-inertial Frames to Gravity: The Equivalence Principle Part II From Curvature to Observations Observational Test of the Equivalence Principle Field Equations in the “vacuum” Test-Particles in the Schwarzschild Space-Time The Classical Tests of General Relativity Gravitational Waves in the “Vacuum” Part III From Singularities to Cosmological Scales Black Holes Field Equations in Non-“Empty” Space-Times Further Applications of the Field Equations Theoretical Cosmology The Hot Big-Bang Appendix A Exercises