An Overview of General Relativity and Space-Time Series in Astronomy and Astrophysics Series

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.

Features

? Provides a self-contained introduction to General Relativity and to its standar applications.

? Presents readers with all the tools necessary for further learning and research in the field.

? Accessible to readers with just foundational knowledge of linear algebra and Lagrangian mechanics.

1. Space and Time: The Classical View. 2. From Space and Time to Space-Time. 3. From Inertial to Non-Inertial Reference Frames. 4. Pseudo-Riemannian Spaces. 5. The Riemann-Christoffel Curvature Tensor. 6. From Non-Inertial Frames to Gravity: the Equivalence Principle. 7. Observational Test of the Equivalence Principle. 8. Field Equations in the "Vacuum": the Isotropic Solution. 9. Test-particles in the Schwarzschild Space-Time. 10. The Classical Tests of General Relativity. 11. Gravitational Waves in the "Vacuum". 12. Schwarzschild Black Holes. 13. Field Equations in Non-Empty Space-Times. 14. Further Applications of Some Field Equations. 15. Theoretical Cosmology. 16. The Hot Big-Bang. Appendix A. References. Index.

Nicola Vittorio is full professor of Astronomy and Astrophysics at the Physics Department of the University of Rome ``Tor Vergata’’. He carried out theoretical studies in cosmology and in the formation and evolution of the large-scale structure of the universe. He published 250 articles on refereed journals, and also was the organizer and the editor of several conferences and conference proceedings. Nicola Vittorio is the Scientific Coordinator of the national ASI/LiteBIRD Project, financed by the Italian Space Agency-ASI to support the participation of the Italian community to the Phase A activities of the JAXA-led LiteBIRD satellite. He is the President of the Board that coordinates the PhD activities of ``Tor Vergata’’ University, the coordinator of the PhD program in Astronomy, Astrophysics and Space Science (run jointly by the Universities of Rome ``Tor Vergata’’ and Sapienza with the National Institute of Astrophysics-INAF) and the Coordinator of the Erasmus Mundus Joint Master program in Astrophysics and Space Science-MASS (run jointly by the universities of Rome "Tor Vergata", Belgrade, Bremen, and Côte d’Azur). Nicola Vittorio is National Fellow of the Academy of Sciences of Turin, Distinguished Member of the Italian Physical Society, Member of the European Academy of Sciences and Arts, of the European Physical Society, of the International Astronomical Union, of the Italian Astronomical Society, and of the Italian Society for the Advancement of Science.